This is my first post to MHF. I'm taking an introductory stats course at college, and I have a problem from a sample exam that's giving me some difficulty. I was hoping that someone might be able to offer some assistance. Thank you.
Problem: A simple random sample of 15-year-old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population w/ a mean equal to 149 lbs. Assume that the standard deviation of the weights of all 15-year-old boys in the city is known to be 16.2 lbs. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), and conclusion.
147, 138, 162, 151, 134, 189, 157, 144, 175, 127, 164
So, as I understand this question, this is what I have so far:
n = 11
x̄ = 153.45
s = 16.2
α = 0.01
Ho: p = 149 (original claim)
H1: p ≠ 149 (counter claim)
Za/2 = -2.575 and 2.575
Test Statistic: Z = p̂p / √pq / n
I understand that p̂ = x/n, but I don't understand what x is in this problem. Any help would be greatly appreciated. Thank you!