A sporting goods store believes the average age of its customers is 37 or less.

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 39.5 years. Assume the standard deviation for customer age is 7.0 years. Using alpha = 0.10, 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. H_0: mu H_1: mu The z-test statistic is (Round to two decimal places as needed.) The critical z-score(s) is(are) (Round to two decimal places as needed. Use a comma to separate answers as needed.) Because the test statistic the null hypothesis. b. Determine the p-value for this test. The p-value is (Round to three decimal places as needed.)

Explanation / Answer

Given that population mean= u = 37, Sample size = 40, Xbar = 39.5, population standard deviation = 7

and level of significance = 0.10

a.

The null and alternative hypothesis is,

H0: µ 37 vs H1: µ > 37

Hence z-statistic = Xbar - µ / (/sqrt(n) ) = 39.5 - 37 / 7/sqrt(40) = 2.26

The critical z-score for = 0.10 is 1.28

Becuase the test statistic (z-statistic = 2.26) is greater than 1.28 (z-score), Hence Reject the null hypothesis.

b. Determine p-value

the p-value is, P(Z > 2.26) = 0.012

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.