To study the effects of an advertising campaign at a supply chain, several store
ID: 3172535 • Letter: T
Question
To study the effects of an advertising campaign at a supply chain, several stores are randomly selected with the following observed before- and after-advertising monthly sales revenues: Let mu_1 be the mean of old sales revenues and mu_2 be the mean of new sales revenues, both in millions of dollars per month. At the level of significance alpha = 0.05, test H_0: mu_1 greaterthanorequalto mu__2 versus H_1: mu_1 greaterthanorequalto mu_2. Sketch the test. Interpret your results in part (a). Sketch and find the p-value of the test. Would you reject H_0 if alpha = 0.06?Explanation / Answer
Store Number
Old sales revenue
New sales revenue
Di
Di-D
Di-D^2
1
6.7
7.2
0.5
0.08
0.0064
2
5.7
5.9
0.2
-0.22
0.0484
3
7.4
7.3
-0.1
-0.52
0.2704
4
5.2
6.3
1.1
0.68
0.4624
5
8.1
8.5
0.4
-0.02
0.0004
Mean
0.42
ED/n
S.D
0.44384682
EDi-D^2/n-1
a)
tSTAT=D-µD/SD/n
0.42-0/0.4438/5
0.42/0.4438/2.236
tSTAT=2.116
b)
tCRIT is 2.7764 and hence it does not lie within the rejection region. Hence, we cannot reject null hypothesis.
c)
The two-tailed P value equals 0.1018.
2.1319 is tCRIT at a=0.06 and tSTAT=2.116. Hence, we cannot reject null hypothesis
Store Number
Old sales revenue
New sales revenue
Di
Di-D
Di-D^2
1
6.7
7.2
0.5
0.08
0.0064
2
5.7
5.9
0.2
-0.22
0.0484
3
7.4
7.3
-0.1
-0.52
0.2704
4
5.2
6.3
1.1
0.68
0.4624
5
8.1
8.5
0.4
-0.02
0.0004
Mean
0.42
ED/n
S.D
0.44384682
EDi-D^2/n-1
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