Question

The mean of math SAT scores is 500 and the standard deviation is 100. A random sample of 64 students from Leeds H.S. received an average of 480. Conduct a hypothesis test to determine if the population mean SAT score for Leeds H.S. is less than 500 with alpha = .05. Determine a p-value and explain it.
I know I need a one-tail test.

Answer 1

Yes, you are correct. This will be a one-tailed test (the alternate hypothesis shows a specific direction on a one-tailed test). Use a z-test. See your other post for an example on calculating the z-test statistic using a z-test.

Your hypotheses for this problem:
Ho: µ = 500 -->null hypothesis
Ha: µ < 500 -->alternate hypothesis

The p-value is the actual level of the test statistic which you can find using a z-table. Compare with .05 to determine whether or not to reject the null. If you reject the null, then you can conclude µ < 500.

I hope this will help get you started.