Question

Data from the Office for National Statistics show that the mean age at which men in Great Britain get married was 32.5. A news reporter noted that this represents a continuation of the trend of waiting until a later age to wed. A new sample of 47 recently wed British men provided their age at the time of marriage. These data are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Open spreadsheet

Do these data indicate that the mean age of British men at the time of marriage exceeds the mean age in 2013? Test this hypothesis at . What is your conclusion? Use the obtained rounded values in your calculations.

Sample mean:	years (to 2 decimals)
Sample standard deviation:	years (to 4 decimals)
-value:	(to 3 decimals)
-value (Two Tail):	(to 3 decimals)

Because -value _________≤> , we _________rejectfail to reject . There is _________insufficientsufficient evidence to conclude that the mean age at which British men get married exceeds what it was in 2013.

Age
33
39
40
40
38
30
35
32
29
34
25
25
34
28
32
39
33
38
30
27
32
25
28
34
29
29
39
30
31
30
26
38
34
27
29
34
35
35
35
37
27
40
31
30
36
26
35

Answer 1

SAMPLE MEAN= 32.40

SAMPLE STANDARD DEVIATION= 4.4996

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 32.532.5

Ha: μ > 32.532.5

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is tc​=1.679.

The rejection region for this right-tailed test is R=t:t>1.679

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis: Since it is observed that t=−0.152≤tc​=1.679, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.560, and since p=0.560≥0.05, 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 32.5, at the 0.05 significance level.