Question

In a random sample of 29 residents living in major cities on the West Coast (Group 1) and 29 residents living in major cities on the East Coast (Group 2), each individual was asked their age. The results can be seen in the table below. The population standard deviation of the age in West Coast cities is known to be 10.95 years and in East Coast cities is known to be 9.67 years. Assume the populations are normally distributed. Run a test at a 0.05 level of significance to test if west coast cities are, on average, older.

West Coast (Group 1)	East Coast (Group 2)
25	35
47	45
18	37
38	20
30	19
52	26
52	79
61	46
43	29
22	55
34	25
35	35
55	36
60	53
68	41
20	50
34	32
36	38
37	26
42	44
60	19
71	28
54	27
20	18
45	30
52	21
34	22
58	43
64	61

Enter the test statistic - round to 4 decimal places.

Test Statistic z =   

Answer 1

For testing hypothesis, we will be using Independent sample z test.

For doing hypothesis test, first we need to find mean age for sample. We have used MS Excel to calculate the mean for both the group.

Steps followed for hypothesis testing are as follows:

Test Statistic z = 2.8855

(5) Conclusion

At 0.05 significance level, there is enough evidence to conclude that residents living in west coast cities are, on average, older.