Question

A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and “big box” discount stores. She suspects the variability is different between those stores due to the nature of the customers involved. To investigate this issue in detail, she compiled two random samples, each consisting of 26 purchase amounts at shopping mall stores (sample 1) and discount stores (sample 2).

Shopping Mall Store Purchase	Discount Store Purchase
214	113
56	94
155	86
272	41
63	124
139	77
213	110
177	150
80	192
241	64
108	120
295	82
82	95
231	47
159	161
90	133
163	88
191	39
207	97
98	133
195	114
99	71
153	107
187	94
212	100
133	92

a. Select the hypotheses to test whether the variance of the purchase amounts differs between the two types of stores.

• H₀: σ1² / σ2² = 1, H_A: σ1² / σ2² ≠ 1

• H₀: σ1² / σ2² ≤ 1, H_A: σ1² / σ2² > 1

• H₀: σ1² / σ2² ≥ 1, H_A: σ1² / σ2² < 1

b. Construct the 95% confidence interval for the ratio of the population variances. Assume that purchase amounts are normally distributed. (Round "F" value and final answers to 2 decimal places.)

Confidence interval is________ to_______.

c. Use the confidence interval to test whether the variance of the purchase amounts differs between the two stores at the 5% significance level.

The 95% confidence interval (contains, does not contain) the value 1, we (reject, do not reject) Ho and conclude that the population variances in purchase amounts are (different, not different) between shopping mall stores and 'big box" retail stores.

d-1. Find the p-value.

• p-value < 0.01

• p-value  0.10
• 0.05  p-value < 0.10
• 0.02  p-value < 0.05
• 0.01  p-value < 0.02

d-2. Confirm your conclusion by finding the p-value.

Thus, our conclusion _________with the confidence interval approach in Part c.

• agrees

• do agree

Answer 1