In: Statistics and Probability
21customers were monitored before and after a large marketing campaign by a large retailer to determine if their spending increased after the campaign, compared to what the spent before the advertising campaign. (Use the 0.05 level of significance).
amount spent (dollars) | |
before | after |
77.19 | 125.85 |
87.13 | 67.12 |
95.17 | 76.79 |
64.44 | 49.06 |
88.95 | 66.45 |
78.3 | 55.21 |
43.69 | 63.57 |
70.33 | 55.09 |
41.74 | 107.72 |
84.14 | 56.71 |
68.52 | 87.03 |
59.97 | 66.89 |
66.03 | 69.1 |
93.39 | 77.45 |
59.46 | 89.04 |
90.41 | 80.36 |
71.44 | 60.81 |
114.89 | 96.31 |
73.59 | 67.32 |
102.95 | 104.88 |
106.38 | 128.45 |
1. What is your null and alternative hypothesis?
2. What is you p-value?
3. What is the conclusion?
necessary calculation table:-
before (xi) |
after (yi) |
||
77.19 | 125.85 | -48.66 | 2307.477 |
87.13 | 67.12 | 20.01 | 425.7537 |
95.17 | 76.79 | 18.38 | 361.1444 |
64.44 | 49.06 | 15.38 | 256.1216 |
88.95 | 66.45 | 22.5 | 534.7101 |
78.3 | 55.21 | 23.09 | 562.3443 |
43.69 | 63.57 | -19.88 | 370.8012 |
70.33 | 55.09 | 15.24 | 251.6602 |
41.74 | 107.72 | -65.98 | 4271.433 |
84.14 | 56.71 | 27.43 | 787.0157 |
68.52 | 87.03 | -18.51 | 319.9162 |
59.97 | 66.89 | -6.92 | 39.64213 |
66.03 | 69.1 | -3.07 | 5.983894 |
93.39 | 77.45 | 15.94 | 274.3595 |
59.46 | 89.04 | -29.58 | 838.4615 |
90.41 | 80.36 | 10.05 | 113.93 |
71.44 | 60.81 | 10.63 | 126.648 |
114.89 | 96.31 | 18.58 | 368.7859 |
73.59 | 67.32 | 6.27 | 47.52448 |
102.95 | 104.88 | -1.93 | 1.706158 |
106.38 | 128.45 | -22.07 | 459.9395 |
sum=-13.1 | sum=12725.3579 |
sample size (n) = 21
a).hypothesis:-
where,
b).test statisic be:-
df = (n-1) = (21-1) = 20
p value be:-
[ in any blank cell of excel type =T.DIST(-0.1133,20,TRUE)]
c).decision:-
p avlue = 0.4555 > 0.05 (alpha)
so, we fail to reject the null hypothesis.
we conclude that,
there is not significant evidence to claim that their spending increased after the campaign, compared to what they spent before the advertising campaign at 0.05 level of significance.
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