Question 1091201: For a particular clothing store, the claim is that the (population) mean age for all customers is 40 years old with a (population) standard deviation of 6.5 years. The store manager feels that the average age is much different than 40 years old. A survey of 30 randomly selected customers gives a sample mean of 37.84 years. Let α =0.10.
(a) What is the level of significance?
(b) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed,or two-tailed test?
(c) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
(d) What is the value of the sample test statistic?
(e) Find (or estimate) the P-value.
(f) Based on your answers in parts (a) to (e), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(g) State your conclusion in the context of the application.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a. 0.10
b. Ho: ages =
Ha: ages aren't equal
Two-tailed.
c. z-test since sigma is known. Assuming normality and random sample.
d. test statistic is z=(x bar-mean)/sigma/sqrt(n)
Critical value is |z|>1.645
value is (37.84-40)/(6.5/sqrt(30)
=-2.16*sqrt(30)/6.5=-1.82
reject Ho, p-value is 0.0687 (calculator, but table would work).
At the 6% significance level the average age is not 40.
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