AnswersAlgebra IIStatistics and Probability — TestQuestion 10
10
QuizMultiple Choice

Statistics and Probability — Test

Question 10 • Algebra II

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is 150 point 0 0 dollars with a standard deviation of 30 point 2 0 dollars The manager collects 40 random receipts and finds that the average is 160 dollars Complete a hypothesis test with a significance level of 2 point 5 percent 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 manager should decrease prices in his store.
B
The customers in his store just come from a rich neighborhood.
C
The customers do not spend more than the national average in his store.
D
The customers spend more than the national average in his store.

Explanation

The hypotheses are H₀: μ = $150 and Hₐ: μ > $150. With a known standard deviation, the test statistic is z = (160 − 150)/(30.20/√40) ≈ 2.09. For a one-tailed test at the 2.5% significance level, the critical value is about 1.96; since 2.09 is larger, reject H₀. The test provides evidence that customers spend more than the national average in this store, so the valid conclusion is “The customers spend more than the national average in his store.”

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