Can you please explain how to conduct a full hypothesis test using the p value method for the scenario below. Make sure all the steps are there.I believe the null hypothesis to be Ho: u = $7,229 and the alt hypothesis to be Ho: u < $7,2229. But im getting mixed up on how to solve for the others. Please help

A sample of 349 account balances of a credit company showed a mean customer balance of $7,082, but the marketing manager claimed that the mean balance for the population was $7,229. The marketing manager said the population standard deviation was $162. Use the p-value approach to conduct a full hypothesis test (all steps) that can be used to determine whether the mean of all account balances is significantly different from $7,229. Let= .05.

The null hypothesis is

The alternative hypothesis is

This test is (choose 1: one-tailed / two-tailed) because the last sentence contains the words (choose 1: greater than/ less than / different from).

I will use a (choose 1: t/z) in my formula because

I have calculated the value of t (or z) to be

I have used t (or z) to get the value of p (most likely from a chart or computer printout - provide that printout).

My p value is

Alpha, which is given in the problem, is

When I compared p to alpha, p is (choose 1: greater than/less than) alpha.

Because of this, I know I should (choose 1: reject / fail to reject) my null hypothesis.