Does being told whether water is from the tap or bottled influence how people rate how good

Question:

Does being told whether water is from the tap or bottled influence how people rate how good it tastes? Student researchers set out to answer this question. In a blind taste test, they asked 31 subjects to rate the taste of two waters, one bottled and one tap, without telling them anything about the waters (the control), on a scale of 1 to 7, with 7 being great tasting and 1 being awful. They repeated this with 31 different subjects but told them which sample was tap and which was bottled (truth condition). They then repeated this one more time with 31 more subjects, but this time they lied to the subjects and told them the tap water sample was bottled water and the bottled water sample was tap (lie condition). The 93 subjects were randomly assigned to one of these conditions. The summary statistics are shown in the following table, and the data are shown in the dotplots. These statistics are based on the difference in each subject’s real bottled water rating minus their real tap water rating. So they shows how much higher participants rated the real bottled water than the real tap water.

The data file BottledWater2 contains the results where the difference is each subject’s real bottled water rating minus their real tap water rating. So it shows how much higher participants rated the real bottled water than the real tap water. Is there strong evidence of an association between what a person is told and how he or she rates the bottled and tap waters?

a. We want to determine whether there is strong evidence of an association between what a person is told and how he or she rates the bottled and tap waters. Use words to state the null and alternative hypotheses for this test.

b. Using the summary statistics given, compute the Mean Group Diff statistic.

c. A null distribution for this study follows. Using the Mean Group Diff statistic you calculated in part (b), will the p-value for this test be large or small? Explain.

d. Does it appear there is an association between what a person is told about the waters and how they rate the bottled and tap waters? If there is an association, can we conclude what participants are told causes the difference? Explain

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