Do people think bottled water tastes better than tap water? In a blind taste test, student researchers asked 31 subjects to rate the taste of two waters, one bottled and one tap, on a scale from 1 to 7, with 7 being great tasting and 1 being awful tasting. The average rating for the bottled water was 4.065 (SD = 1.504), the average rating for the tap water was 4.032 (SD = 1.741), and the differences had a mean of 0.032 (SD = 1.975). The researchers randomly determined the order that the subjects tasted each water by flipping a coin so that some tasted tap water first and some tasted bottled water first. Here are the hypotheses. 

H₀: In the long run, people will rate bottled water and tap water the same, on average (μ_d = 0). 

H_a: In the long run, people will rate bottled water higher than tap water, on average (μ_d > 0). 

a. What are the explanatory and response variables in this study and what types of variables are they (categorical or quantitative)?

b. Is this an observational study or a randomized experiment? 

c. What is the observed statistic for this study? 

d. Assuming a true null hypothesis, we simulated this study and found 5,000 mean differences that are shown in the null distribution shown in the Exercise 7.2.18d output. Based on where the observed statistic lies in the distribution, does the p-value appear to be fairly small? 

e. What is the standardized statistic for this test? 

f. Based on the standardized statistic from part (e), is there strong evidence that people prefer the taste of bottled water? Explain.

 

Transcribed Image Text:

Mean 0.000 SD = 0.349 1.20 0.80 0.40 0.00 Average difference 0.40 0.80 1.20