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: Ho: TT = 0.4 HA: IT # 0.4 Gail is given a sample and calculates the test statistic. Using a level of significance of a = 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 a = 0.1, while Ben uses a = 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. Reject Doesn't reject Cannot tell a) Andrew O O O b) Ben O O OApril is a statistics student who has extensive computer programming skills. She programs a randomrnumber generator that produces numbers that follow the normal distribution with mean u = 14 (her favorite number) and standard deviation 0 = 4. April's friend Augustus does not know that the population mean is 14. However he knows that April's favorite number is 14, and decides to conduct a hypothesis test with the followmg hypotheses: H0: p = 14 HA: p : 14 The result of the test is that Augustus does not reject the null hypothesis. Augustus has: committed a Type I error committed a Type II error not committed a Type I error or Type I] error committed both a Type I error and a Type II error 0000 Select whether the following changes to a hypothesis test will cause the value of B to increase, decrease or remain unchanged. In each case, assume all other aspects of the test remain the same. Increase Decrease Unchanged a) A larger level of Cl is selected for the test. 0 O O b) There is a decrease in the magnitude of the critical value(s). 0 O O c) A larger sample size is selected for the test. 0 O O