Aresearcher 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 with a standard deviation of 6.4 years. test the researcher’s claim using α = 0.10.
a. state and label the null and alternate hypotheses.
b. state the critical value(s) for this test and draw a picture of the critical region(s).
c. find the value of the test statistic.
d. find the p-value for this test.
e. find an appropriate confidence interval to use to test this hypothesis. state the confidence level used.
f. 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.