Question

you have been asked to study the mean amount of financial aid awarded to a population of students at a certain university. You are interested in making some decisions concerning this population parameter. You select a random sample of 38 students from this population. The mean amount of financial aid awarded to these students in the year being studied is $17,055. You have reason to believe that the population standard deviation of the amounts of financial aid awarded is thought to equal $7,000. At both the 5% and 10% levels of significance, is the mean financial aid awarded to this population of students different from $15,000? In your discussion, if appropriate, comment upon the effect of the change in the significance level on your decision.

Answer 1

Given 17055 n = 38 $ 7000 10 = $15000 Null Mypothesis, Ho: 4 = 15000 Alternative Hypothesis Hy y = 15000 (two feriled text Test statistic : The test statistic under Ho, 7-4 Zeal NN(0,1) nis large? alin Frad 17055-15ooo Fooo J38 2055 T135.55 Izcall - 7.87 Critical value: Ab x = 0.05 : Critical value for two tailed test isz=1.96 Sinle We Hypothesis Tcall < Za fail to rejeet Null LL means that mean financial aid awarded to the population is not different from $ 15000 Sl. level of significance

At X=0:10 : Critical value for two teiled test is 1.64 Since -1.96 -1.64 1.64 1.8/ 196 1Zcat/ 71.64 We reject the wall Hypothesis. that mean financial aid awarded the population is different from $15000. at 10% level of significance means It te
Here we can see level of significance plays a crucial role in making the decision.

At 5% level of significance we failed to reject the null hypothesis but same hypothesis we rejected at 10% level of significance.