question 2Give the rejection region.Group of answer choicesz greater than 1.64t greater than 1.64z greater than 1.58t greater than 1.58 question 3Give the test statistic.Group of answer choicesz = 1.64t = 1.58t = 1.64z = 1.58 question 4 Give the conclusion.Group of answer choicesReject the null since the test statistic is not in the rejection region.Fail to reject the null since the test statistic is not in the rejection region. A comparative study is done between students who study more than 12hours for a final exam and those that study less than 12 hours for a finalexam. The average final exam score of 200 students that studied morethan 12 hours is 84% with a standard deviation of 20%. The average finalexam score of 200 students that studied less than 12 hours is 79% with astandard deviation of 40%. At the 5% significance level determine if theaverage grade of those that study more than 12 hours is higher than thosethat don't. Take the students that study more than 12 hours as population1.Give the hypotheses.O Null: There is no difference in the average grade between those that study morethan 12 hours and those that do not.Alternative: The average grade of those that study more than 12 hours is higherthan those that do not.O Null: There is no difference in the average grade between those that study morethan 12 hours and those that do not.Alternative: The average grade of those that study more than 12 hours is lessthan those that do not.O Null: There is no difference in the average grade between those that study morethan 12 hours and those that do not.Alternative: The average grade of those that study more than 12 hours for a finalis not equal to those that do not.

Given Data : For Sample 1 x̄1 = 84.0 s1 = 20.0 n1 = 200 For Sample 2 x̄2 = 79.0 s2 = 40.0 n2 = 200 Significance level, α= 0.05Solution : 1) Hypothesis test : The null and alternative hypothesis is Ho : u1-u2 = 0.0 Ha : u1-u2 > 0.0 Null: There is no difference in the average grade between those that study more than 12 hours and those that do not. Alternative: The average grade of those that study more than 12 hours is higher than those that do not. Option A is correct2) Degree of freedom = 292.6471 = 292 Degree of freedom is 292 critical value : critical value at α = 0.05 tα= 1.64 Decision rule Reject Ho if t > 1.64 Answer - option C3) Test statistic = ( 84.0 - 79.0 )/(v(( 20.0 ^2/ 200 )+( 40.0 ^2/ 200 )) = 1.581 The test statistic is 1.58 Option B is correct4) As t < 1.65 we fail to reject the null hypothesis Decision : Fail to reject the null since the test statistic is not in the rejection region. Option B is correct.