Question

For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly customer arrival rates is 8 customers or less, then a fixed number of checkout lanes can be staffed without excessive customer waiting time or excessive clerk idle time. However, before determining how many checkout lanes (and thus clerks) to use, she must verify that the standard deviation of the arrival rates does not exceed 8. Accordingly, a sample of 25 hourly customer arrival rates was compiled for that shift over the past week.

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a. Select the hypotheses to test whether the standard deviation of the customer arrival rates exceeds 8.

• H₀: σ² ≤ 64; H_A: σ² > 64

• H₀: σ² = 64; H_A: σ² ≠ 64

• H₀: σ² ≥ 64; H_A: σ² < 64

b. Calculate the value of the test statistic. Assume that customer arrival rates are normally distributed. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

d-1. At α = 0.05, what is your conclusion?

d-2. Would your conclusion change at the 1% significance level?

• Yes

• No

Answer 1

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