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 9 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 9. Accordingly, a sample of 25 hourly customer arrival rates was compiled for that shift over the past week.

a. Select the hypotheses to test whether the standard deviation of the customer arrival rates exceeds 9.

• H₀: σ² ≤ 81; H_A: σ² > 81

• H₀: σ² = 81; H_A: σ² ≠ 81

• H₀: σ² ≥ 81; H_A: σ² < 81

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.)

Test Statistic: ???

Hourly Arrival Rates
122
122
101
119
91
115
112
111
118
124
122
122
124
122
121
125
116
93
124
105
132
93
121
112
114

Answer 1

a).hypothesis:-

necessary calculation table:-

Hourly Arrival Rates(x)
122	45.6976
122	45.6976
101	202.7776
119	14.1376
91	587.5776
115	0.0576
112	10.4976
111	17.9776
118	7.6176
124	76.7376
122	45.6976
122	45.6976
124	76.7376
122	45.6976
121	33.1776
125	95.2576
116	0.5776
93	494.6176
124	76.7376
105	104.8576
132	280.8976
93	494.6176
121	33.1776
112	10.4976
114	1.5376
sum=2881	sum = 2848.56

so, the sample variance be:-

b).test statistic:-

  

= 35.167

degrees of freedom = (25-1) = 24

p value = 0.066 ( using p value calculator for chi square = 35.167, df = 24)

decision:-

p value = 0.066 > 0.05

[ here, no level of significance is mentioned, so i have considered alpha = 0.05]

so, we don't have enough evidence to reject the null hypothesis at 0.05 level of significance

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