Question

Gail is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are: H0: p = 0.4 Ha: p ≠ 0.4 Gail is given a sample and calculates the test statistic. Using a level of significance of α = 0.05, she does not reject the null hypothesis. Gail's friends, Andrew and Ben, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Andrew uses a level of significance of α = 0.1, while Ben uses α = 0.01. All three students perform their calculations correctly. For each of Gail's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given.

Answer 1

H0: p = 0.4

Ha: p ≠ 0.4

Gail uses a level of significance of α = 0.05, she does not reject the null hypothesis.

therefore the p-value she obtained is greater than 0.05

Andrew uses a level of significance of α = 0.1

Since from given information we can not say if p value is > 0.1 or less, hence

it is impossible to tell from the information given.

Ben uses α = 0.01

Since p-value is greater than 0.05 hence definitely greater than 0.01

does not reject the null hypothesis.