9
practice testMultiple Choice

Practice Test

Question 9 • Mathematics III

Kavita has been assigned the task of studying the average customer receipt for a branch of a major restaurant chain. The average receipt for the chain is $⁢72.00 with a standard deviation of $⁢11.00. The branch she is studying has an average bill of $⁢67.00 for the last 40 receipts. She needs to know if this falls below the chain’s average. She will use a 1% level for significance because she does not want to inadvertently report the restaurants income as below average. Upper-Tail Values A 5 percent 2 point 5 percent ​1% Critical z -v alues 1 point 6 5 1 point 9 6 2 point 5 8 Which choice depicts the result for Kavita’s hypothesis test?

Answer
A
She should reject ratio of cap h sub 0 to mu is equal to 72 and accept ratio of cap h sub A to mu is less than 72 .
B
She should reject ratio of cap h sub 0 to mu is equal to 72 and accept ratio of cap h sub A to mu is not equal to 72 .
C
She should reject ratio of cap h sub A to mu is less than 72 but cannot accept ratio of cap h sub 0 to mu is equal to 72 .

Explanation

The hypotheses are H₀: μ = $72 and Hₐ: μ < $72. The test statistic is z = (67 − 72)/(11/√40) ≈ −2.88, which is below the 1% lower-tail critical value (about −2.33), so the result is significant. Kavita should reject H₀; the result supports the alternative that the branch’s average receipt is below $72, matching choice B.

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