Concerned with the increase of plastic water bottles in landfills, a leading environmentalist wants to determine whether there is any difference in taste between the local tap water and the leading bottled water. She randomly selects 14 consumers and conducts a blind taste test. She asks the consumers to rank the taste on a scale of one to five (with "five" indicating excellent taste). The sample results are shown in the accompanying table.

a. Using the sign test, specify the competing hypotheses to determine whether there are significant differences in preferences between tap water and bottled water.
b. Calculate the value of the test statistic.
c. Calculate the p-value.
d. At the 5% significance level, what is the conclusion?
Do the results indicate that significant differences exist in preferences?

Transcribed Image Text:

Tap Bottled Consumer Water WaterConsumer Water Water Tap Bottled 4 10 4 3 3 12 13 14 3 6