Question

13. A researcher claims that the average age of a woman when she has her first child is still equal to the 1993 mean of 27.1 years. She obtains a random sample of 30 women who had their first child this year and finds the sample mean age to be 28.2 years. Suppose the population standard deviation is 6.4 years. Test the researcher’s claim using α = 0.10.

1. State and label the null and alternate hypotheses. (2 points)

2. State the critical value(s) for this test and draw a picture of the critical region(s). (3 points)

3. Find the value of the test statistic. (3 points)

4. Find the P-value for this test. (3 points)

5. Find an appropriate confidence interval to use to test this hypothesis. State the confidence level used. (4 points)

6. State your conclusion of this hypothesis test, citing reasons from all three methods. Be sure to explain your conclusion in the context of the problem. (5 points)

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = 0.9414

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

P value = 2 * P ( Z > 0.9414 ) = 0.3465

Decision based on P value
P value = 2 * P ( Z > 0.9414 ) = 0.3465
Reject null hypothesis if P value < level of significance
P - value = 0.3465 > 0.10 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Confidence Interval :-



Lower Limit =
Lower Limit = 26.278
Upper Limit =
Upper Limit = 30.122
90% Confidence interval is ( 26.278 , 30.122 )

Since lies in the interval, hence we fail to reject null hypothesis

There is sufficient evidence to support the claim that the average age of a woman when she has her first child is still equal to the 1993 mean of 27.1 years 10% level of significance.