Question

a study of student’s attitudes towards college varies on a scale from 0 to 180 and has a mean µ = 118 and a standard deviation σ = 19. The null and alternative hypotheses I wish to test are: H_o: μ=118 against H_a: μ>118 One sample of 24 students had a sample mean of x-bar = 124.7.

Find the exact p-value associated with this sample (hint: you'll need to use the normal distribution table).

A .0418

B  .9140

C  .9582

D 1.65

Part b What conclusion do you draw about this test at α = .02 level?

A. Reject H_o

B. Accept H_o

C. Fail to reject H_o

D. Inconclusive

Part c Another sample of 24 different students had the sample mean x - bar = 127.8. Find the test statistic value.

A. 2.53

B. 12.38

C. 2.78

D. .52

Part d, find the pair of p-values that bracket the test statistic value from above.

A. .005 and .0025

B. .01 and .005

C. .02 and .01

D. .04 and .02

Part e, what conclusion do you draw at the α = .01 level?

A. Accept H_o

B. It is statistically significant

C. It is not statistically significant

D. It cannot be determined

Answer 1

The provided sample mean is Xˉ=124.7

and the known population standard deviation is σ=19,

and the sample size is n = 24.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=118

Ha: μ>118

(2) Rejection Region

Based on the information provided, the significance level is α=0.02,

and the critical value for a right-tailed test is

z_c = 2.05

The rejection region for this right-tailed test is

R={z:z>2.05}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that

z=1.728≤zc​=2.05,

it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is p = 0.0418, and

since p =0.0418 ≥ 0.02,

it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is greater than 118, at the 0.02 significance level.

The provided sample mean is Xˉ=127.8

and the known population standard deviation is σ=19,

and the sample size is n = 24.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=118

Ha: μ>118

(2) Rejection Region

Based on the information provided, the significance level is α=0.01,

and the critical value for a right-tailed test is

z_c = 2.33

The rejection region for this right-tailed test is

R={z:z>2.33}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that

z=2.527>zc​=2.33,

it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value is p = 0.0058,

and since p=0.0058 < 0.01,

it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 118, at the 0.01 significance level.