Test the claim that the mean GPA of night students is smaller than 2.5 at the 0.02 significance level. a.) The null and alternative hypothesis would be: Ho:u 2.5 Ho: / 2 2.5 Ho:p = 0.625 Ha: p > 2.5 Ha:u 0.625 O O O b.) The test is: left-tailed right-tailed two-tailed O O Based on a sample of 80 people, the sample mean GPA was 2.46 with a sample standard deviation of 0.02 c.) The test statistic is: (to 3 decimals) d.) The p-value is: (Use Excel and round to 4 decimals) e.) Based on this we: O Reject the null hypothesis because p > o O Reject the null hypothesis because p aYou wish to test the following claim (Ha) at a significance level of a = 0.05. Ho: u = 89.4 Ha: u # 89.4 (Claim) You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 91 with mean c = 96.5 and a standard deviation of $ = 16.5. a.) What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = b.) What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = (use Excel) c.) The p-value is... O greater than a O less than (or equal to) or d.) This test statistic leads to a decision to... O reject the null hypothesis O accept the null hypothesis O fail to reject the null hypothesis e.) As such, the final conclusion is that... O There is not sufficient sample evidence to support the claim that the population mean is not equal to 89.4. The sample data support the claim that the population mean is not equal to 89.4.A local politician claims that the percentage of residents over the age of 25 who have bachelor's degrees is less than 40%. At the .01 significance level, test her claim. a.) The null and alternative hypothesis would be: Ho:p = 0.4 Ho:/ = 0.4 Ho:p = 0.4 Ha:p > 0.4 Ha:/ 0.4 Ha :p / 0.4 Ha : u # 0.4 O O b.) The test is: left-tailed right-tailed two-tailed O O O Based on a sample of 75 local residents over the age of 25, 31% possessed a bachelor's degree c.) This excercise is a hypothesis test for the... O Proportion using the Z-test statistic O Mean with the population standard deviation unknown using the t-test statistic OProportion using the t-test statistic O Mean with the population standard deviation known using the Z-test statistic O Mean with the population standard deviation unknown using the Z-test statistic O Mean with the poulation standard deviation known using the t-test statisticunknown using the Z-test statistic O Mean with the poulation standard deviation known using the t-test statistic d.) The test statistic is: (to 2 decimals) e.) At o = .01, the critical value is: (to 3 decimals) f.) Based on this we: O Fail to reject the null hypothesis. There is NOT enough evidence to support the claim of the politician that the percentage of residents over the age of 25 who have bachelor's degrees is less than 40% O Fail to reject the null hypothesis. There is NOT enough evidence to reject the claim of the politician that the percentage of residents over the age of 25 who have bachelor's degrees is less than 40% O Reject the null hypothesis. There is enough evidence to reject the claim of the politician that the percentage of residents over the age of 25 who have bachelor's degrees is less than 40% O Reject the null hypothesis. There is enough evidence to support the claim of the politician that the percentage of residents over the age of 25 who have bachelor's degrees is less than 40%