Question

The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood. Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311. What is the p-value of the test statistic? Answer choices are rounded to the hundredths place.

Answer 1

0.20

Explanation:

In order to find the p-value we first need the degrees of freedom because we are running a t-test. The df = n-1 = 30-1 = 29. If Amy is using the alternative hypothesis, µ ≠ 531, this is a two-tailed test. In order to find the p-value, we simply need to find the probability of being as extreme or more extreme as our current test statistic in one-tail and then multiply it by 2. Another way to describe this is it is the tail probability/area. If we go to the df row of 29 and then scan to the right we see 1.311 is in the 0.10 column. So if we multiply this by 2, we find 0.20 or 20% in both of the tails. So the p-value is 0.20.

Answer 2

0.10

Explanation:

Average age of Iowa residents = 37 years

Amy believes that the average age in her hometown in Iowa is not equal to this average

Alternative hypothesis : µ ≠ 37

Sample size = 30

t - test statistic = 1.311

The p-value of the test statistic can be obtained using the online p-value calculator :

The p- value obtained using a t-test statistic value of 1.311 and a degree of freedom (df =N-1; 30 - 1 = 29) at a 0.05 significance level = 0.100072 = 0.10 ( nearest hundredth)