Question

Multiple Choice

The average age of becoming a mother has increased dramatically over the last 50 years. A researcher is interested in knowing if it has stayed the same over the last 5 years. Therefore, the researcher took a random sample of 75 birth records for Clare County, Wisconsin from 2012 and 2017 and compared them. The statistics for both samples are as follows:

Sample 1: 2012	Sample 2: 2017
Average Age:   28.17	Average age:   29.93
Std Dev. (s1):                 9.1	Std Dev. (s1):               9.7
Sample size (n1):         75	Sample size (n1):       75

1. Assuming a 2 sided t-test with an alpha of 0.05, what is the t statistic for this test?

a) -1.1500

b) -1.9762

c) 1.1500

d) 1.9762

2. Assuming a 2 sided t-test with an alpha of 0.05, over the last 5 years has the average age of becoming a mother changed?

a) Yes the age has changed, reject the null hypothesis

b) Yes the age has changed, fail to reject the null hypothesis

c) No the age has not changed, reject the null hypothesis

d) No the age has not changed, fail to reject the null hypothesis

Answer 1

Part 1:

To Test:-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-


t = -1.1500
Test Criteria :-
Reject null hypothesis if | t | > t(α/2, DF)


DF = 147
Critical value t(α/2, DF) = t(0.05 /2, 147 ) = 1.9762 (from t-table)
| t | > t(α/2, DF) = 1.1500 < 1.9762
Result :- Fail to Reject Null Hypothesis

Part 2:

d) No the age has not changed, fail to reject the null hypothesis