Question

Home Shopping Network, Inc., pioneered the idea of merchandising directly to customers through cable television. The Network hired a new show hostess for their cosmetic products at the beginning of this year. The marketing director of the Network wants to know whether the average sales of the cosmetic products has increased after the new show hostess was hired. The director selected a random sample of 40 viewers, and examined their spending on the cosmetic products during the holiday season of the previous year and the same period of the current year. The paired observations for each shopper are given in an Excel file, Quiz 1 (DATA). Click the file name to download it.

Shopper   Previous Year's Shopping ($)   Current Year's Shopping ($)
1   297.02   170.00
2   255.95   431.00
3   457.17   426.17
4   176.40   275.39
5   281.91   426.55
6   407.78   491.20
7   239.91   263.02
8   355.73   481.47
9   349.17   340.00
10   544.19   227.86
11   301.46   273.66
12   340.42   199.95
13   359.44   381.84
14   315.50   538.00
15   409.16   428.63
16   313.13   439.46
17   239.36   485.75
18   363.55   315.39
19   376.67   191.18
20   149.00   535.23
21   451.06   313.20
22   407.80   224.26
23   345.36   278.35
24   248.01   211.63
25   289.36   292.44
26   227.01   241.31
27   218.13   395.49
28   226.73   350.52
29   247.58   352.09
30   169.64   351.59
31   306.62   410.73
32   268.47   476.55
33   398.44   261.78
34   259.87   558.72
35   304.59   436.67
36   224.53   380.78
37   270.02   553.78
38   308.52   379.88
39   256.93   355.98
40   179.70   476.54

The director wants to know at α = 5 % if the new show hostess increases the average sales of the cosmetics products. Let μ d be the average difference in spending calculated from the previous year’s amount minus the current year’s amount.

Step 1: State the hypotheses of the test.

Group of answer choices

H_o: , H_a:

H_o: , H_a:

H_o: , H_a:

H_o:  H_a:

H_o: , H_a:

Step 2: Find the test statistic. Give your answer to 3 decimal places.

Step 3: Find the P-value of the test. Give your answer to 3 decimal places.

Step 4: A 95% confidence interval for μ d is

Answer 1

mean dbar=	d̅                           =	-62.0688
degree of freedom =n-1                            =		39.000
Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		153.449
std error=Se=SD/√n=		24.2624
test statistic            =	(d̅-μd)/Se         =	-2.5582

step 1:

null Hypothesis:μd		>=	0
alternate Hypothesis: μd		<	0

step 2:

test statistic =-2.558

step 3:

p value

=

0.007

step 4)

for 95% CI; and 39 degree of freedom, value of t=			2.023
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		49.075
lower confidence limit                     =		-111.1441
upper confidence limit                    =		-12.9934
from above 95% confidence interval for population mean =(-111.144,-12.993)