The Pvalue in Example 176 is the probability taking the null

The P-value in Example 17.6 is the probability (taking the null hypothesis = 0 to be true) that x takes a value at least as far from 0 in either direction as 17. For this exercise, x= 17, = 60 and the sample size is 18.

Step 1:
What is the sampling distribution of x when = 0?

Step 2:
Do a Normal probability calculation to find the P-value.

Solution

What is the sampling distribution of x when = 0?

mean = 0

sigma = 60 / 18 = 3.333

Normal with mean 0 and standard deviation 3.3333.

P value

Z = 17 - 0 / 3.333

Z = 5.10

p value