Question

A sporting goods store believes the average age of its customers is 37 or less. A random sample of 40 customers was​ surveyed, and the average customer age was found to be 40.2 years. Assume the standard deviation for customer age is 9.0 years. Using alphaequals0.10​, complete parts a and b below.

a. Does the sample provide enough evidence to refute the age claim made by the sporting goods​ store?

Determine the null and alternative hypotheses. Upper H 0​: mu ▼ equals not equals less than less than or equals greater than or equals greater than nothing Upper H 1​: mu ▼ not equals less than greater than equals greater than or equals less than or equals nothing

b. The critical z scores is/are?

c. determine the p value for this test. Should this be rejected?

Answer 1

We are using z test because population standard deviation is known.

From given information,

Population Mean μ = 37

Population standard deviation σ = 9

Sample size n= 40

Sample mean Xbar = 40.2

1. Null Hypothesis H_{0 :} μ ≤ 37

Alternative Hypothesis is H_{1 :} μ > 37

2. Z critical value for one tail at α=0.10  Z_c = 1.28

Decision rule: We reject H₀ when Z > 1.28

Test statistics

Z score =

Z = (40.2 - 37) / (9/sqrt(40)) = 2.249

Here Z = 2.249 > 1.28 so we reject null hypothesis at 10 % level of significance.

3. P value = P(Z < 2.249) = 1 - NORM.S.DIST(2.249,TRUE) = 1 - 0.9877 = 0.0123

Here P value = 0.0123 < 0.10 so we reject null hypothesis.

Conclusion: There is no sufficient evidence to claim that a sporting goods store believes the average age of its customers is 37 or less at 10% level of significance.