Question

Suppose a credit card company wants to examine the difference between credit card spending on groceries and leisure. To do so, it generates a paired sample of 7 credit card customers’ spending in each category. Assume spending in each area is normally distributed. Data are in thousands.

Groceries	Leisure
10.0	4.3
2.2	2.7
9.9	11.2
9.4	9.4
8.0	3.4
10.8	2.5
10.5	10.5

1. If the credit card company believes the population difference in spending is $4,500 (4.5), test whether the mean spending difference in the sample is different from the population mean. Use a .05 level of significance.
2. What is the 95% confidence interval for the difference in spending?
3. Why is a paired sample better than an unpaired sample when testing hypotheses concerning the difference between two population means

Answer 1

(a)

Following table shows the difference x:

Groceries	Leisure	x = Groceries - Leisure
10	4.3	5.7
2.2	2.7	-0.5
9.9	11.2	-1.3
9.4	9.4	0
8	3.4	4.6
10.8	2.5	8.3
10.5	10.5	0

Following table shows the calculations for mean and SD:

	X	(X-mean)^2
	5.7	10.89
	-0.5	8.41
	-1.3	13.69
	0	5.76
	4.6	4.84
	8.3	34.81
	0	5.76
Total	16.8	84.16

Conclusion: There is no evidence that the mean spending difference in the sample is different from the population mean.

(b)

(c)

Here we need to compare whether a person more on groceries than liesure so paired data should be used.