1 In a twotailed test for the population mean the null hypot

1. In a two-tailed test for the population mean, the null hypothesis will be rejected at alpha level of significance if the value of the test statistic z is such that:

A. -z_a <|z|<Z_a
B. |z|>Z_a
C. |z|<Z_a/2
D. |z|>Z_a/2

2. A professor of mathematics refutes the claim that the average student spends 4.5 hours studying for the final comprehensive exam. To test the claim, the hypothesis: Ho:mu=4.5 vs Ha: mu not equal to 4.5, should be used.

A. True
B. False

Solution

1. a two-tailed test for the population mean, at alpha level of significance is a combination of right tailed and left tailed test.

for right tailed test the null hypothesis is rejected at alpha level of significance if the value of the test statistic z is such that z>Z_a

for left tailed test the null hypothesis is rejected at alpha level of significance if the value of the test statistic z is such that z<-Z_a

so for two tailed test to retain alpha level of significance the critical point is chosen as Z_a/2

and the null hypothesis is rejected if the test statistic z is such that

z<-Z_a/2 and z>Z_a/2 or |z|>Z_a/2

hence the correct option is option D. |z|>Z_a/2 [answer]

2. the professor wants to test whether the average hours a student spends studying for the final comprehensive exam is 4.5 hours or not.

there is nothing like whether the average hours a student spends studying for the final comprehensive is greather than 4.5 hours or less than 4.5 hours.

so the test should be a two tailed test.

hence the hypothesis to be used should be

Ho:mu=4.5 vs Ha: mu not equal to 4.5

hence the correct option is A. TRUE [answer]