QUIZ HELP: Null and Alternate Hypothesis, P-value, critical value and test statistic

#1
My quiz is due tomorrow and 10% of my grade. I need help doing it because I'm pretty sure I have no idea what I'm doing.

The first question is

A researcher claims that the average age of a woman before she has her first child is greater than the 1990 mean age of 26.2 years, on the basis of data obtained from the National Vital Statistics Report, volume 48, number 14.
She obtains a simple random sample of 13 women who gave birth to their first child in 1999 and finds the sample mean age to be 27.1 years. The population standard deviation is 6.4 years. Test the researcher’s claim using alpha = .05 level of significance.


a. State the null and the alternate hypotheses

Ho: ___________________and Ha: ___________________


b. State the critical value(s) for this test. ________________


c. Find the test statistic. ___________________



d. Find the p-value for this test. ______________________


e. State your conclusion in the context of this problem.



I got Ho: μ ≤ 26.2 and Ha: is 26.2 ≤ μ

Critical Value: 1.96

For the test statistic I did

(27.1-26.2) / (6.4) = .140625

P-value 0.195

I don't think this is right at all. I need to show the work too.