Hypothesis Testing HW

So on the hypothesis testing question, I can get everything right except for the actual p-value.

For example:

You wish to test the following claim (Ha) at a significance level of α=0.01
Ho:μ=82.5
Ha:μ>82.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=23 with mean M=86.1 and a standard deviation of SD=15.9

My calculations:
SE = 15.9/sqrt(23)
z = (86.1-82.5)/SE = 1.0858
p-val = 1-0.8621 = 0.1379

This value us greater than the alpha value, so we fail to reject the null and conclude that there is not sufficient sample evidence to support the claim that the population mean is greater than 82.5.

All of my answers are correct except the actual p-value. Any help?

I’ve been having the same problem, and I can’t figure it out either.

This is my bad! Here’s the short story: The sample size of 23 is too small to use a normal distribution. There is another distribution, called the t-distribution that we will learn about soon that adjusts for small sample size. Sorry about that!