Question

We wish to compare the PsyCap scores of our class to a predetermined standard set by a study conducted in 2014. The population mean for this standard is 121. 58 with a standard deviation of 11.29.  

Utilizing the steps of hypothesis testing, determine if the scores of our class are equal to those of the standard using a 95% confidence level.

28	33	32	31	124
30	22	33	22	107
32	29	31	27	119
20	24	29	30	103
24	23	27	32	106
32	33	33	29	127
29	22	27	24	102
36	30	32	29	127
23	17	21	21	82
36	22	36	24	118
24	29	26	25	104
21	26	29	19	95
26	21	24	24	95
27	28	31	27	113

Answer

Step 1

Our Hypothesis

Ho: Ho =   μ = 121.58 (equal to(null))

Ha: μ ≠ 121.58 (not equal to (alternative))

Step 2

Specify the significance level a(alpha)

a = 0.05

Step 3   (also step 5)

Select the test statistic (two tailed test, this means two rejecting regions)

     (103.76-121.58)/ 11.29/ square root of 17 = -6.507

                                   0.95

0.025                                                                0.025

               -1.96                                      1.96

Step 4

The rule is to decide whether the z equals that of Ho, if it is less or more we reject and favor the alternative Ha

Step 5

     (103.76-121.58)/ 11.29/ square root of 17 = -6.507

                                   0.95

0.025                                                                0.025

               -1.96                                      1.96

Step 6 Decide whether to reject Ho

Because the result was -6.507, we choose to reject Ho

Step 7

We conclude that scores are below 2014’s data, meaning it is not equal.

Answer 1