A researcher wants to study the impact of a new artificial sweetener on blood glucose. He is designing an experiment in which participants will have a drink either with or without the sweetener and then have their blood glucose measured. He wants to test the null hypothesis that the average blood glucose is the same for the two drinks. Consider the following two experimental designs. Experiment 1: Two hundred participants are randomly assigned to receive either the drink with the sweetener or the drink without the sweetener, with 100 assigned to each group. In this case the researcher has 200 measurements: 100 from the artificial sweetener group, and 100 from the no artificial sweetener group. Experiment 2: One hundred participants each have both drinks, but on subsequent days. The first day, they are randomized to receive one of the drinks, and then have their glucose measured. The second day, they receive the other drink, then they have their glucose measured again. In this case the researcher also has 200 measurements: 100 from the participants measured on the day they received the artificial sweetener, and 100 from the same participants measured on the day they received the drink with no artificial sweetener. Hypothetically, the researcher could construct the two-sample z-statistic we discussed in class in each of these cases. Is it appropriate to use this test statistic in Experiment 1? (circle one) YES NO Briefly explain your choice. Is it appropriate to use this test statistic in Experiment 2? (circle one) YES NO Briefly explain your choice.
A researcher wants to study the impact of a new artificial sweetener on blood
glucose. He is designing an experiment in which participants will have a drink either
with or without the sweetener and then have their blood glucose measured. He
wants to test the null hypothesis that the average blood glucose is the same for the
two drinks.
Consider the following two experimental designs.
Experiment 1: Two hundred participants are randomly assigned to receive either the
drink with the sweetener or the drink without the sweetener, with 100 assigned to
each group. In this case the researcher has 200 measurements: 100 from the
artificial sweetener group, and 100 from the no artificial sweetener group.
Experiment 2: One hundred participants each have both drinks, but on subsequent
days. The first day, they are randomized to receive one of the drinks, and then have
their glucose measured. The second day, they receive the other drink, then they
have their glucose measured again. In this case the researcher also has 200
measurements: 100 from the participants measured on the day they received the
artificial sweetener, and 100 from the same participants measured on the day they
received the drink with no artificial sweetener.
Hypothetically, the researcher could construct the two-sample z-statistic we
discussed in class in each of these cases.
Is it appropriate to use this test statistic in Experiment 1? (circle one) YES NO
Briefly explain your choice.
Is it appropriate to use this test statistic in Experiment 2? (circle one) YES NO
Briefly explain your choice.
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