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

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

3. 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

Solution :

Given that

To 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 so suppose the population standard deviation is 6.4 years. Test the researcher’s claim using α = 0.10.