13
practice testMultiple Choice

Practice Test

Question 13 • 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 point 0 0 dollars with a standard deviation of 11 point 0 0 dollars The branch she is studying has an average bill of 67 point 0 0 dollars for the last 40 receipts. She needs to know if this falls below the chain’s average. She will use a 1 percent 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 not equal to 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 less than 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

Use a lower-tail z-test with H₀: μ = $72 and Hₐ: μ < $72. The test statistic is z = (67 − 72) ÷ (11 ÷ √40) ≈ −2.88. At the 1% significance level, the lower-tail critical value is −2.58; since −2.88 is smaller, reject H₀. The result supports the conclusion that the branch’s average receipt is below $72, matching choice C.

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