Question

15) Are shoppers more or less likely to use credit cards for "impulse purchases" that they decide to make on the spot, as opposed to purchases that they had in mind when they went to the store? Stop every third person leaving a department store with a purchase. (This is in effect a random sample of people who buy at that store.) A few questions allow us to classify the purchase as impulse or not. Here are the data on how the customer paid: (HINT: you will need the sample sizes of each group) Credit Card? Yes No Impulse purchases 13 18 3 Planned purchases 35 31 66 a) Estimate with 95% confidence the proportion of credit card users at this department store.

Answer 1

Answer:

For impulse, 95% CI = (0.2456, 0.5931)

Confidence Interval Estimate for the Proportion
Data
Sample Size	31
Number of Successes	13
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.4194
Z Value	-1.9600
Standard Error of the Proportion	0.0886
Interval Half Width	0.1737
Confidence Interval
Interval Lower Limit	0.2456
Interval Upper Limit	0.5931

For planned, 95% CI = (0.4099, 0.6507)

Confidence Interval Estimate for the Proportion
Data
Sample Size	66
Number of Successes	35
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.5303
Z Value	-1.9600
Standard Error of the Proportion	0.0614
Interval Half Width	0.1204
Confidence Interval
Interval Lower Limit	0.4099
Interval Upper Limit	0.6507

b).

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	13
Sample Size	31
Group 2
Number of Items of Interest	35
Sample Size	66
Intermediate Calculations
Group 1 Proportion	0.4194
Group 2 Proportion	0.5303
Difference in Two Proportions	-0.1109
Average Proportion	0.4948
Z Test Statistic	-1.0192
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.3081
Do not reject the null hypothesis

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	95%
Intermediate Calculations
Z Value	-1.9600
Std. Error of the Diff. between two Proportions	0.1078
Interval Half Width	0.2114
Confidence Interval
Interval Lower Limit	-0.3223
Interval Upper Limit	0.1004

95% CI for difference = (-0.3223, 0.1004)

c).

95% CI for difference for proportion (-0.3223, 0.1004) contains 0 value. Therefore there is no difference between the two proportions.

d).

P value = 0.3081