AnswersGA-Advanced Algebra Concepts and Connections CRUnit Test — Unit testQuestion 17
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Unit Test — Unit test

Question 17 • GA-Advanced Algebra: Concepts and Connections CR

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?

Answer
A
The customers spend more than the national average in his store.
B
The manager should decrease prices in his store.
C
The customers do not spend more than the national average in his store.
D
The customers in his store just come from a rich neighborhood.

Explanation

Test whether the mean exceeds $150: the null hypothesis is μ = $150 and the alternative is μ > $150. The standard error is $30.20/√40 ≈ $4.78, so the test statistic is ($160 − $150)/$4.78 ≈ 2.09. For a one-tailed test at the 2.5% significance level, the critical z-value is about 1.96; since 2.09 is greater, reject the null hypothesis. The valid conclusion is that the customers spend more than the national average in his store.

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