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Luke’s Lab Partner(s) For his statistics project, Luke is performing a hypothesi

ID: 3153067 • Letter: L

Question

Luke’s Lab Partner(s) For his statistics project, Luke is performing a hypothesis test to compare the proportion of people in Austin that have tattoos to the proportion in the rest of the United States (the true proportion of U.S. adults with a tattoo is believed to be 21%, according to a recent Harris Poll). Based on a survey that Luke conducts in downtown Austin, he calculates a z-statistic of +1.40.

a) Since Luke believes Austin to be “weird” and thinks that the proportion of Austin adults with a tattoo will be greater than that for the rest of the country, his alternative hypothesis is “Ha: p > 0.21”. Based on the zscore that he calculated and his alternative hypothesis, calculate the p-value for Luke’s hypothesis test.

b) Luke’s lab partner, Ciara, thinks that Austin adults will have a lower proportion of tattoos than the rest of the States, so she sets her alternative hypothesis as “Ha: p < 0.21”. Based on the same z-score of 1.40 (since she used the same data as Luke), calculate the p-value for Ciara’s hypothesis test.

c) Marie is a friend of Luke and Ciara, and while she is not even taking Statistics, decides to join in on the fun. Marie decides to use the same data to perform a two-tailed test (so her alternative hypothesis is “p 0.21”). Using the same z-score as Luke and Ciara, calculate the p-value for Marie’s hypothesis test.

Explanation / Answer

Luke’s Lab Partner(s) For his statistics project, Luke is performing a hypothesis test to compare the proportion of people in Austin that have tattoos to the proportion in the rest of the United States (the true proportion of U.S. adults with a tattoo is believed to be 21%, according to a recent Harris Poll). Based on a survey that Luke conducts in downtown Austin, he calculates a z-statistic of +1.40.

a) Z = 1.40 p value : 0.0608

b)

p value : 0.0608 * 2 = 0.1216