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Answer:
Test statistics = 2.85
P-value = 0.002
Step-by-step explanation:
We are given that a sporting goods store believes the average age of its customers is 38 or less.
A random sample of 40 customers was surveyed, and the average customer age was found to be 41.6 years and the standard deviation for customer age is 8.0 years.
Null Hypothesis, :
<= 38 years
Alternate Hypothesis, :
> 38 years
The test statistics we will use here is;
T.S. = ~ N(0,1)
where, X bar = sample mean = 41.6 years
= population standard deviation = 8 years
n = sample size = 40
So, test statistics = = 2.85
At 5% level of significance, the z table gives critical value of 1.6449. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject the null hypothesis and conclude that average age of its customers is more than 38 years.
P-value is given by, P(Z > 2.85) = 1 - P(Z <= 2.85) = 1 - 0.99781 = 0.002 .