state the null hypothesis about oreo cookies

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Investigation: Oreo Cookie Lab with Stats

This introductory lab introduces students to the concept of hypothesis testing. Students determine if Double Stuff Oreo cookies really do contain double the amount of stuffing.

The student worksheet contains instructions and a walk-through on how to do standard deviation calculations.

This is a fun and “tasty” lab this is simple to conduct. Students have already learned how to calculate standard error using a sample set of data. Now, they simply scrape the filling out of the cookies and weigh the mass to compare the regular to double stuff.

Then, they create a graph and add error bars to show either reject or accept their hypothesis based on the degree of overlap between the error bars. I have done this lab every year and consistently find that double stuff Oreos really do have double the amount of stuffing!

The final task is completing a Claim Evidence Reasoning chart.

Example of Reasoning:

The double stuff Oreos had double the filling. The data show that on average the Oreos that were double stuff had 26 g of filling while the regular ones had only 12 g of filling. The graph shows that if the data were doubled, the mean for the regular Oreos would be just under the mean for the double stuff Oreos, 24 g. The 2 SEM bar overlap shows that with 95% confidence, the means are similar between the double stuff and the doubled regular Oreo data set, therefore, we fail to reject the null hypothesis.

Shannan Muskopf

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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11.2: Correlation Hypothesis Test

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The correlation coefficient, \(r\), tells us about the strength and direction of the linear relationship between \(x\) and \(y\). However, the reliability of the linear model also depends on how many observed data points are in the sample. We need to look at both the value of the correlation coefficient \(r\) and the sample size \(n\), together. We perform a hypothesis test of the "significance of the correlation coefficient" to decide whether the linear relationship in the sample data is strong enough to use to model the relationship in the population.

The sample data are used to compute \(r\), the correlation coefficient for the sample. If we had data for the entire population, we could find the population correlation coefficient. But because we have only sample data, we cannot calculate the population correlation coefficient. The sample correlation coefficient, \(r\), is our estimate of the unknown population correlation coefficient.

• The symbol for the population correlation coefficient is \(\rho\), the Greek letter "rho."
• \(\rho =\) population correlation coefficient (unknown)
• \(r =\) sample correlation coefficient (known; calculated from sample data)

The hypothesis test lets us decide whether the value of the population correlation coefficient \(\rho\) is "close to zero" or "significantly different from zero". We decide this based on the sample correlation coefficient \(r\) and the sample size \(n\).

If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is "significant."

• Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is significantly different from zero.
• What the conclusion means: There is a significant linear relationship between \(x\) and \(y\). We can use the regression line to model the linear relationship between \(x\) and \(y\) in the population.

If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is "not significant".

• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is not significantly different from zero."
• What the conclusion means: There is not a significant linear relationship between \(x\) and \(y\). Therefore, we CANNOT use the regression line to model a linear relationship between \(x\) and \(y\) in the population.
• If \(r\) is significant and the scatter plot shows a linear trend, the line can be used to predict the value of \(y\) for values of \(x\) that are within the domain of observed \(x\) values.
• If \(r\) is not significant OR if the scatter plot does not show a linear trend, the line should not be used for prediction.
• If \(r\) is significant and if the scatter plot shows a linear trend, the line may NOT be appropriate or reliable for prediction OUTSIDE the domain of observed \(x\) values in the data.

PERFORMING THE HYPOTHESIS TEST

• Null Hypothesis: \(H_{0}: \rho = 0\)
• Alternate Hypothesis: \(H_{a}: \rho \neq 0\)

WHAT THE HYPOTHESES MEAN IN WORDS:

• Null Hypothesis \(H_{0}\) : The population correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship(correlation) between \(x\) and \(y\) in the population.
• Alternate Hypothesis \(H_{a}\) : The population correlation coefficient IS significantly DIFFERENT FROM zero. There IS A SIGNIFICANT LINEAR RELATIONSHIP (correlation) between \(x\) and \(y\) in the population.

DRAWING A CONCLUSION:There are two methods of making the decision. The two methods are equivalent and give the same result.

• Method 1: Using the \(p\text{-value}\)
• Method 2: Using a table of critical values

In this chapter of this textbook, we will always use a significance level of 5%, \(\alpha = 0.05\)

Using the \(p\text{-value}\) method, you could choose any appropriate significance level you want; you are not limited to using \(\alpha = 0.05\). But the table of critical values provided in this textbook assumes that we are using a significance level of 5%, \(\alpha = 0.05\). (If we wanted to use a different significance level than 5% with the critical value method, we would need different tables of critical values that are not provided in this textbook.)

METHOD 1: Using a \(p\text{-value}\) to make a decision

Using the ti83, 83+, 84, 84+ calculator.

To calculate the \(p\text{-value}\) using LinRegTTEST:

On the LinRegTTEST input screen, on the line prompt for \(\beta\) or \(\rho\), highlight "\(\neq 0\)"

The output screen shows the \(p\text{-value}\) on the line that reads "\(p =\)".

(Most computer statistical software can calculate the \(p\text{-value}\).)

If the \(p\text{-value}\) is less than the significance level ( \(\alpha = 0.05\) ):

• Decision: Reject the null hypothesis.
• Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is significantly different from zero."

If the \(p\text{-value}\) is NOT less than the significance level ( \(\alpha = 0.05\) )

• Decision: DO NOT REJECT the null hypothesis.
• Conclusion: "There is insufficient evidence to conclude that there is a significant linear relationship between \(x\) and \(y\) because the correlation coefficient is NOT significantly different from zero."

Calculation Notes:

• You will use technology to calculate the \(p\text{-value}\). The following describes the calculations to compute the test statistics and the \(p\text{-value}\):
• The \(p\text{-value}\) is calculated using a \(t\)-distribution with \(n - 2\) degrees of freedom.
• The formula for the test statistic is \(t = \frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}\). The value of the test statistic, \(t\), is shown in the computer or calculator output along with the \(p\text{-value}\). The test statistic \(t\) has the same sign as the correlation coefficient \(r\).
• The \(p\text{-value}\) is the combined area in both tails.

An alternative way to calculate the \(p\text{-value}\) ( \(p\) ) given by LinRegTTest is the command 2*tcdf(abs(t),10^99, n-2) in 2nd DISTR.

THIRD-EXAM vs FINAL-EXAM EXAMPLE: \(p\text{-value}\) method

• Consider the third exam/final exam example.
• The line of best fit is: \(\hat{y} = -173.51 + 4.83x\) with \(r = 0.6631\) and there are \(n = 11\) data points.
• Can the regression line be used for prediction? Given a third exam score ( \(x\) value), can we use the line to predict the final exam score (predicted \(y\) value)?
• \(H_{0}: \rho = 0\)
• \(H_{a}: \rho \neq 0\)
• \(\alpha = 0.05\)
• The \(p\text{-value}\) is 0.026 (from LinRegTTest on your calculator or from computer software).
• The \(p\text{-value}\), 0.026, is less than the significance level of \(\alpha = 0.05\).
• Decision: Reject the Null Hypothesis \(H_{0}\)
• Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (\(x\)) and the final exam score (\(y\)) because the correlation coefficient is significantly different from zero.

Because \(r\) is significant and the scatter plot shows a linear trend, the regression line can be used to predict final exam scores.

METHOD 2: Using a table of Critical Values to make a decision

The 95% Critical Values of the Sample Correlation Coefficient Table can be used to give you a good idea of whether the computed value of \(r\) is significant or not . Compare \(r\) to the appropriate critical value in the table. If \(r\) is not between the positive and negative critical values, then the correlation coefficient is significant. If \(r\) is significant, then you may want to use the line for prediction.

Example \(\PageIndex{1}\)

Suppose you computed \(r = 0.801\) using \(n = 10\) data points. \(df = n - 2 = 10 - 2 = 8\). The critical values associated with \(df = 8\) are \(-0.632\) and \(+0.632\). If \(r <\) negative critical value or \(r >\) positive critical value, then \(r\) is significant. Since \(r = 0.801\) and \(0.801 > 0.632\), \(r\) is significant and the line may be used for prediction. If you view this example on a number line, it will help you.

Exercise \(\PageIndex{1}\)

For a given line of best fit, you computed that \(r = 0.6501\) using \(n = 12\) data points and the critical value is 0.576. Can the line be used for prediction? Why or why not?

If the scatter plot looks linear then, yes, the line can be used for prediction, because \(r >\) the positive critical value.

Example \(\PageIndex{2}\)

Suppose you computed \(r = –0.624\) with 14 data points. \(df = 14 – 2 = 12\). The critical values are \(-0.532\) and \(0.532\). Since \(-0.624 < -0.532\), \(r\) is significant and the line can be used for prediction

Exercise \(\PageIndex{2}\)

For a given line of best fit, you compute that \(r = 0.5204\) using \(n = 9\) data points, and the critical value is \(0.666\). Can the line be used for prediction? Why or why not?

No, the line cannot be used for prediction, because \(r <\) the positive critical value.

Example \(\PageIndex{3}\)

Suppose you computed \(r = 0.776\) and \(n = 6\). \(df = 6 - 2 = 4\). The critical values are \(-0.811\) and \(0.811\). Since \(-0.811 < 0.776 < 0.811\), \(r\) is not significant, and the line should not be used for prediction.

Exercise \(\PageIndex{3}\)

For a given line of best fit, you compute that \(r = -0.7204\) using \(n = 8\) data points, and the critical value is \(= 0.707\). Can the line be used for prediction? Why or why not?

Yes, the line can be used for prediction, because \(r <\) the negative critical value.

THIRD-EXAM vs FINAL-EXAM EXAMPLE: critical value method

Consider the third exam/final exam example. The line of best fit is: \(\hat{y} = -173.51 + 4.83x\) with \(r = 0.6631\) and there are \(n = 11\) data points. Can the regression line be used for prediction? Given a third-exam score ( \(x\) value), can we use the line to predict the final exam score (predicted \(y\) value)?

• Use the "95% Critical Value" table for \(r\) with \(df = n - 2 = 11 - 2 = 9\).
• The critical values are \(-0.602\) and \(+0.602\)
• Since \(0.6631 > 0.602\), \(r\) is significant.
• Conclusion:There is sufficient evidence to conclude that there is a significant linear relationship between the third exam score (\(x\)) and the final exam score (\(y\)) because the correlation coefficient is significantly different from zero.

Example \(\PageIndex{4}\)

Suppose you computed the following correlation coefficients. Using the table at the end of the chapter, determine if \(r\) is significant and the line of best fit associated with each r can be used to predict a \(y\) value. If it helps, draw a number line.

• \(r = –0.567\) and the sample size, \(n\), is \(19\). The \(df = n - 2 = 17\). The critical value is \(-0.456\). \(-0.567 < -0.456\) so \(r\) is significant.
• \(r = 0.708\) and the sample size, \(n\), is \(9\). The \(df = n - 2 = 7\). The critical value is \(0.666\). \(0.708 > 0.666\) so \(r\) is significant.
• \(r = 0.134\) and the sample size, \(n\), is \(14\). The \(df = 14 - 2 = 12\). The critical value is \(0.532\). \(0.134\) is between \(-0.532\) and \(0.532\) so \(r\) is not significant.
• \(r = 0\) and the sample size, \(n\), is five. No matter what the \(dfs\) are, \(r = 0\) is between the two critical values so \(r\) is not significant.

Exercise \(\PageIndex{4}\)

For a given line of best fit, you compute that \(r = 0\) using \(n = 100\) data points. Can the line be used for prediction? Why or why not?

No, the line cannot be used for prediction no matter what the sample size is.

Assumptions in Testing the Significance of the Correlation Coefficient

Testing the significance of the correlation coefficient requires that certain assumptions about the data are satisfied. The premise of this test is that the data are a sample of observed points taken from a larger population. We have not examined the entire population because it is not possible or feasible to do so. We are examining the sample to draw a conclusion about whether the linear relationship that we see between \(x\) and \(y\) in the sample data provides strong enough evidence so that we can conclude that there is a linear relationship between \(x\) and \(y\) in the population.

The regression line equation that we calculate from the sample data gives the best-fit line for our particular sample. We want to use this best-fit line for the sample as an estimate of the best-fit line for the population. Examining the scatter plot and testing the significance of the correlation coefficient helps us determine if it is appropriate to do this.

The assumptions underlying the test of significance are:

• There is a linear relationship in the population that models the average value of \(y\) for varying values of \(x\). In other words, the expected value of \(y\) for each particular value lies on a straight line in the population. (We do not know the equation for the line for the population. Our regression line from the sample is our best estimate of this line in the population.)
• The \(y\) values for any particular \(x\) value are normally distributed about the line. This implies that there are more \(y\) values scattered closer to the line than are scattered farther away. Assumption (1) implies that these normal distributions are centered on the line: the means of these normal distributions of \(y\) values lie on the line.
• The standard deviations of the population \(y\) values about the line are equal for each value of \(x\). In other words, each of these normal distributions of \(y\) values has the same shape and spread about the line.
• The residual errors are mutually independent (no pattern).
• The data are produced from a well-designed, random sample or randomized experiment.

Linear regression is a procedure for fitting a straight line of the form \(\hat{y} = a + bx\) to data. The conditions for regression are:

• Linear In the population, there is a linear relationship that models the average value of \(y\) for different values of \(x\).
• Independent The residuals are assumed to be independent.
• Normal The \(y\) values are distributed normally for any value of \(x\).
• Equal variance The standard deviation of the \(y\) values is equal for each \(x\) value.
• Random The data are produced from a well-designed random sample or randomized experiment.

The slope \(b\) and intercept \(a\) of the least-squares line estimate the slope \(\beta\) and intercept \(\alpha\) of the population (true) regression line. To estimate the population standard deviation of \(y\), \(\sigma\), use the standard deviation of the residuals, \(s\). \(s = \sqrt{\frac{SEE}{n-2}}\). The variable \(\rho\) (rho) is the population correlation coefficient. To test the null hypothesis \(H_{0}: \rho =\) hypothesized value , use a linear regression t-test. The most common null hypothesis is \(H_{0}: \rho = 0\) which indicates there is no linear relationship between \(x\) and \(y\) in the population. The TI-83, 83+, 84, 84+ calculator function LinRegTTest can perform this test (STATS TESTS LinRegTTest).

Formula Review

Least Squares Line or Line of Best Fit:

\[\hat{y} = a + bx\]

\[a = y\text{-intercept}\]

\[b = \text{slope}\]

Standard deviation of the residuals:

\[s = \sqrt{\frac{SSE}{n-2}}\]

\[SSE = \text{sum of squared errors}\]

\[n = \text{the number of data points}\]

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The way the cookie crumbles: researchers study the science behind Oreos

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Posted: 20 April 2022 | Abi Sritharan (New Food) | No comments yet

A research team from MIT has put an Oreo’s cream filling through a series of tests to understand why the cream sticks to just one side.

There are many ways to eat the humble Oreo: you can dunk it in your hot drink, you can eat it as it is, or you can twist it apart where one side will be smothered in cream whilst the other side is plain. But why is it that the cookie’s cream sticks to just one wafer when twisted apart? Researchers from the Massachusetts Institute of Technology (MIT) in the US set out to try and solve this conundrum. 

To figure out the mystery, the team subjected cookies to standard rheology tests in the lab and found that no matter the flavour or amount of stuffing, the cream at the centre of an Oreo almost always sticks to one wafer when twisted open. Only for older boxes of cookies does the cream sometimes separate more evenly between both wafers. The scientists behind the study have published their research and results in the Physics of Fluid journal . 

“There’s the fascinating problem of trying to get the cream to distribute evenly between the two wafers, which turns out to be really hard,” said Max Fan, an undergraduate in MIT’s Department of Mechanical Engineering.

The researchers also measured the torque required to twist open an Oreo, and found it to be similar to the torque required to turn a doorknob and about one tenth what’s needed to twist open a bottlecap. The cream’s failure stress (the force per area required to get the cream to flow or deform) is twice that of cream cheese and peanut butter, and about the same magnitude as mozzarella cheese. Judging from the cream’s response to stress, the team classifies its texture as “mushy,” rather than brittle, tough, or rubbery.

So, why does the cookie’s cream stick to just one side? The manufacturing process may be to blame, according to the researchers.

“Videos of the manufacturing process show that they put the first wafer down, then dispense a ball of cream onto that wafer before putting the second wafer on top,” said Crystal Owens, an MIT mechanical engineering PhD candidate who studies the properties of complex fluids. “Apparently that little time delay may make the cream stick better to the first wafer.”

In all, the team went through about 20 boxes of Oreos during its study, including various sizes and flavours. They found that no matter flavour or the amount of cream filling, the cream almost always separated onto one wafer.

“We had expected an effect based on size,” Owens said. “If there was more cream between layers, it should be easier to deform. But that’s not actually the case.”

When the researchers noted each cookie’s result to its original position in the box, they noticed the cream tended to stick to the inward-facing wafer: Cookies on the left side of the box twisted such that the cream ended up on the right wafer, whereas cookies on the right side separated with cream mostly on the left wafer. They suspect this box distribution may be a result of post-manufacturing environmental effects, such as heating or jostling that may cause cream to peel slightly away from the outer wafers, even before twisting.

The team’s study not only aimed to find out about the science behind Oreos, but it also seeks to make the science of rheology accessible to others. To that end, the researchers have designed a 3D-printable “Oreometer” — a simple device that firmly grasps an Oreo cookie and uses pennies and rubber bands to control the twisting force that progressively twists the cookie open. The understanding gained from the properties of Oreo cream could also potentially be applied to the design of other complex fluid materials, according to the researchers.

And as for the cream in the cookie, Owens concluded that “as they are now, we found there’s no trick to twisting that would split the cream evenly.”

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Science News Explores

Cookie science 2: baking a testable hypothesis.

Using cookies recipes, I develop a hypothesis you can test in any kitchen

When designing a scientific experiment, it’s important to have an idea you can test by changing just one variable at a time. For cookie science, I will start by looking at different kinds of flour.

B. Brookshire/SSP

Share this:

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By Bethany Brookshire

August 22, 2014 at 8:00 am

This article is one of a series of  Experiments  meant to teach students about how science is done, from generating a hypothesis to designing an experiment to analyzing the results with statistics. You can repeat the steps here and compare your results — or use this as inspiration to design your own experiment. 

Welcome back to Cookie Science, where I’m using cookies to show you that science can be both close to home and quite delicious. I’m going to take you through finding a hypothesis, designing an experiment to test it, analyzing your results and much more.

To design an experiment, we need to start by defining a goal. What concept do we want to understand? What do we want to achieve? In my case, I would like to share a cookie with my friend Natalie. Unfortunately, it’s not as easy as handing her a cookie.

As I noted in part 1 , Natalie has celiac disease. Whenever she tries to eat something with gluten in it, her immune system attacks her small intestine. This causes her a lot of pain. Right now, the only thing she can do about it is avoid gluten. 

Gluten is a pair of proteins found in grains such as the wheat used in baking flour. So this means that flour — and a cookie made from it — are off limits. My goal is to take my favorite cookie recipe and change it into something with gluten-free flour that Natalie can enjoy.

This is a fine goal. But it is not a hypothesis. A hypothesis is an explanation for something occurring in the natural world, from inside Earth to inside our kitchens. But a hypothesis in science is something more. It is a statement that we can prove to be true or false by testing it in a rigorous way. And by rigorous, I mean by changing one factor after another, test-by-test, to measure if and how each change affects the outcome.

“Making my recipe gluten-free” is not a testable hypothesis. To come up with an idea I could work with, I had to do some reading. I compared six cookie recipes. Three contain gluten:

•    The Chewy (by Alton Brown)
•    Chewy Chocolate Chip Cookies (from Food Network Magazine )
•   Chocolate Chip Cookies (from Food Network Kitchen).

Three similar sounding recipes contain no gluten:

•    Gluten-free Double Chocolate Chip Cookies (by Erin McKenna)
•    Soft & Chewy Gluten-Free Chocolate Chip Cookies (by the Minimalist Baker).
•    Gluten-free Chocolate Chip Cookies {The Best!} (by Cooking Classy)

When I read the ingredients list for each recipe carefully, I noticed something. Gluten-free recipes for cookies generally do not just substitute gluten-free flour in place of wheat flour. They also add something else, such as xanthan gum. Gluten is an important ingredient. It gives wheat products their nice spongy texture, something critical for a nice, chewy chocolate chip cookie. It is possible that without gluten, a cookie has a different texture.

Suddenly, I had a hypothesis I could work with.

Hypothesis: Substituting gluten-free flour alone into my cookie dough will not make a cookie that is comparable to my original recipe.

This is an idea that I can test. I can change one variable — gluten-free flour in place of wheat flour — to find out if that changes the cookie and alters its taste.

Come back next time, as I move toward baking up my experiment.

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Power Words

hypothesis  A proposed explanation for a phenomenon. In science, a hypothesis is an idea that hasn’t yet been rigorously tested. Once a hypothesis has been extensively tested and is generally accepted to be the accurate explanation for an observation, it becomes a scientific theory.

gluten   A pair of proteins — gliadin and glutenin — joined together and found in wheat, rye, spelt and barley. The bound proteins give bread, cake and cookie doughs their elasticity and chewiness. Some people may not be able to comfortably tolerate gluten, however, because of a gluten allergy or celiac disease.

statistics  The practice or science of collecting and analyzing numerical data in large quantities and interpreting their meaning. Much of this work involves reducing errors that might be attributable to random variation. A professional who works in this field is called a statistician.

variable  (in experiments)   A factor that can be changed, especially one allowed to change in a scientific experiment. For instance, when measuring how much insecticide it might take to kill a fly, researchers might change the dose or the age at which the insect is exposed. Both the dose and age would be variables in this experiment.          

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Why MIT Researchers Are Studying Oreos

Fluid dynamics experts find that it’s nearly impossible to split the black-and-white cookie’s sweet filling evenly in half

Daily Correspondent

Since childhood, Crystal Owens has been stymied by a lingering question about one of her favorite snack foods: Is it possible to twist an Oreo cookie and split the sweet, creamy filling evenly in half between both chocolate wafers? Now, Owens and other fluid dynamics experts at the Massachusetts Institute of Technology (MIT) think they finally have an answer.

Per a new paper published this week in the journal Physics of Fluid , the researchers suggest that it’s nearly impossible to split Oreo’s famous creme so that half ends up on each wafer.

“In essentially all possible twisting configurations, the creme tends to delaminate from one wafer, resulting in one nearly bare wafer and one with almost all the creme,” Owens tells Vice ’s Becky Ferreira. “In the case that creme ends up on both wafers, it tends to divide in half so that each wafer has a ‘half-moon’ of creme rather than a thin layer, so there is no secret to get creme evenly everywhere just by twisting open—you have to mush it manually if that's what you want.”

The results were surprising, as Owens and her colleagues fully expected to be able to split the creme with some experimental techniques in the lab. To understand the scientific underpinnings of the iconic black-and-white cookie made by Nabisco, they used an instrument known as a rheometer , which twisted the cookie between two plates.

They tested a variety of Oreo filling quantities (such as “Double Stuf” and “Mega Stuf” cookies), tried dipping the cookies in milk and even tweaked the device’s rotation rate, but nothing made a difference: The creme still stuck primarily to one wafer. The researchers attribute this to the Oreo production process, which creates one “creme-heavy side” of each cookie, they write in the paper.

“It turns out there’s not really a trick to it,” Owens tells Popular Science ’s Philip Kiefer. “Everything you try to do will get mostly a clean break. It’s a bit disappointing that there’s not some secret twist.”

In addition to detailing the results of their experiments, they also coined a new field of study: Oreology, which is a mashup of “Oreo” and the Greek phrase “rheo logia,” which means “flow study.” The new field is officially “the study of the flow and fracture of sandwich cookies,” according to the paper.

Importantly for citizen scientists and Oreo-lovers alike, the researchers also developed and tested a new Oreometer that uses rubber bands and coins. They published the instructions for building this 3-D-printed device online.

“When you want to study the fluid mechanics of food, or ‘Fooid Mechanics,’ with scientific rigor, you need a tool to make quantitative measurements,” the researchers write in an introduction to the instructions .

Though studying Oreo cookies may seem trivial, the research could be an important tool for explaining complex fluid dynamics principles used in fields like 3-D printing and a potential gateway for getting new individuals interested in science more broadly.

"When we talk about the physics of complicated materials, and there are many, the Oreo cookie creme is one that is accessible to many people immediately," Randy Ewoldt, a mechanical engineer at the University of Illinois Urbana-Champaign who was not involved in the study, tells CNN ’s Madeline Holcombe. "To bring people into a much more complicated world, this may serve as an entryway for that."

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Sarah Kuta | READ MORE

Sarah Kuta is a writer and editor based in Longmont, Colorado. She covers history, science, travel, food and beverage, sustainability, economics and other topics.

Helping math teachers bring statistics to life

Estimating a Population Mean

Chapter 8 - day 7 - lesson 8.3, all chapters, learning targets.

Determine the critical value for calculating a C% confidence interval for a population mean using a table or technology.

State and check the Random, 10%, and Normal/ Large Sample conditions for constructing a confidence interval for a population mean.

Construct and interpret a confidence interval for a population mean.

Activity: How much does an Oreo weight?

Answer Key:

Nabisco, the company that owns Oreo, claims that the true mean weight of an Oreo cookie is 11.3 grams. In this Activity, students will be using sample data to examine the potential evidence against this claim. You might want to have 30 Oreos in the front of the classroom to make the data more realistic – actually this is just so that each student leaves class with an Oreo. I promise this will help when you are recruiting students for next year’s AP Stats class.

Why t* instead of z*?

Too many students are conditioned to memorize “z* for proportions, t* for means“. While this is true, this statement does not answer the why. The short answer is that when trying to estimate the mean of a population, we also have to estimate the standard deviation of the population in order to understand the standardized distribution of sample means. Because we are now trying to estimate 2 parameters, we are introducing more variation into the standardized statistic. Thus the distribution of sample means follows a t-distribution, which is wider and shorter than a Normal distribution. We will give a more detailed explanation in Section 9.3.

How to satisfy the Normal/Large Sample condition?

There are three potential ways to satisfy the Normal/Large Sample Condition

Easy: If the population distribution is (approximately) Normal, then the sampling distribution of the sample mean is (approximately) Normal.

Medium: If the population distribution is not Normal (or shape is unknown), the sampling distribution of the sample mean is approximately Normal if the sample size is large enough, which is 30 in most cases. Students learned about the Central Limit Theorem in  Section 7.3 .

Hard: If the shape of the population is unknown and the sample size is small, graph the sample data. If the sample data shows no strong skewness and no outliers, it is reasonable to assume the population distribution is approximately Normal (meaning the sampling distribution is approximately Normal).

Inferential Thinking

When we get to Chapter 9, Nabisco’s claim that the mean weight of an Oreo is 11.3 grams will become the null hypothesis. Students will then use the data to determine whether or not we have convincing evidence against this claim by calculating a P-value. We can get students already thinking about this by asking whether or not the confidence interval provides convincing evidence against the claim (it does!).

Oreo Cookie Treatment Lowers LDL Cholesterol More Than High-Intensity Statin therapy in a Lean Mass Hyper-Responder on a Ketogenic Diet: A Curious Crossover Experiment

Affiliations.

• 1 Harvard Medical School, Boston, MA 02115, USA.
• 2 Lipoprotein and Metabolic Disorders Institute, Raleigh, NC 27615, USA.
• PMID: 38276308
• PMCID: PMC10818743
• DOI: 10.3390/metabo14010073

Recent research has identified a unique population of 'Lean Mass Hyper-Responders' (LMHR) who exhibit increases in LDL cholesterol (LDL-C) in response to carbohydrate-restricted diets to levels ≥ 200 mg/dL, in association with HDL cholesterol ≥ 80 mg/dL and triglycerides ≤ 70 mg/dL. This triad of markers occurs primarily in lean metabolically healthy subjects, with the magnitude of increase in LDL-C inversely associated with body mass index. The lipid energy model has been proposed as one explanation for LMHR phenotype and posits that there is increased export and subsequent turnover of VLDL to LDL particles to meet systemic energy needs in the setting of hepatic glycogen depletion and low body fat. This single subject crossover experiment aimed to test the hypothesis that adding carbohydrates, in the form of Oreo cookies, to an LMHR subject on a ketogenic diet would reduce LDL-C levels by a similar, or greater, magnitude than high-intensity statin therapy. The study was designed as follows: after a 2-week run-in period on a standardized ketogenic diet, study arm 1 consisted of supplementation with 12 regular Oreo cookies, providing 100 g/d of additional carbohydrates for 16 days. Throughout this arm, ketosis was monitored and maintained at levels similar to the subject's standard ketogenic diet using supplemental exogenous d-β-hydroxybutyrate supplementation four times daily. Following the discontinuation of Oreo supplementation, the subject maintained a stable ketogenic diet for 3 months and documented a return to baseline weight and hypercholesterolemic status. During study arm 2, the subject received rosuvastatin 20 mg daily for 6 weeks. Lipid panels were drawn water-only fasted and weekly throughout the study. Baseline LDL-C was 384 mg/dL and reduced to 111 mg/dL (71% reduction) after Oreo supplementation. Following the washout period, LDL-C returned to 421 mg/dL, and was reduced to a nadir of 284 mg/dL with 20 mg rosuvastatin therapy (32.5% reduction). In conclusion, in this case study experiment, short-term Oreo supplementation lowered LDL-C more than 6 weeks of high-intensity statin therapy in an LMHR subject on a ketogenic diet. This dramatic metabolic demonstration, consistent with the lipid energy model, should provoke further research and not be seen as health advice.

Keywords: LDL cholesterol; carbohydrates; ketogenic diet; lean mass hyper-responder; lipid energy model.

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