![]() Students should settle on something like the following: They should say a one-tailed test because there is a direction of interest: It is reasonable to assume Double Stuf cookies have more filling. For the alternative hypothesis, ask students if they think a one- or two-tailed test is more appropriate. The next step is to ask students, “What are the null hypotheses for Question 1?” It may help to remind them that null hypotheses tend to state that there is no difference from the mean. Is there evidence that the mean amount of filling in Double Stuf Oreos is twice the mean amount of filling in regular Oreos?.Is there evidence that Double Stuf Oreos and Regular Oreos have different amounts of filling?.I suggest writing the two questions of interest on the board: I pose the question, “How could we establish that Double Stuf Oreos and regular Oreos have different amounts of filling?” If students have been studying t-tests, they should respond with “a t-test!” They might suggest comparing the means, to which you could respond, “What is a statistical method for comparing means?” Students should settle on a t-test for independent samples because we wish to compare whether two groups (filling from regular Oreos filling from Double Stuff Oreos) have different means and the two groups are independent because they are two types of cookie. ![]() Hence I ask students how they could use statistics to establish whether the two types of cookies have different amounts of filling. This is a reasonable assumption to make, but it is also one for which we can provide empirical support. However, we cannot start with this question, because it assumes Double Stuf Oreos have more filling than regular Oreos. Is there evidence that the mean amount of filling in Double Stuf Oreos is twice the mean amount of filling in regular Oreos? The first step in the activity is forming a statistical question. I like to form the statistical questions and a plan for data collection as a class, then have students divide into small groups to collect data. (These prerequisites correspond to Common Core State Standards for Mathematics 6.SP.1, 6.SP.2, 6.SP.5, 7.SP.3, 7.SP.4, S-ID.1, S-ID.2, S-ID.3). Students should also know how to perform and interpret a t-test for two independent samples and the assumptions underlying the test. As such, prerequisite knowledge includes how to make a histogram, compute means, and compute standard deviations. I suggest using the Double Stuffed? Activity ( Figures 1 and 2) after students have learned how to conduct t-tests for two independent samples. Paper, pencils, and calculators (for data collection and calculations).Bowls or paper towels (to hold deconstructed cookies). ![]()
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