Mean comparison with dependent samples To study the effects of an advertising ca
ID: 3130518 • Letter: M
Question
Mean comparison with dependent samples
To study the effects of an advertising campaign at a supply chain, several stores are randomly selected with the following observed before and afteradvertising monthly sale revenues (in millions of dollars): Store number - 1, 2, 3, 4, 5 Old sale revenue(mil. of dollars) - 7.3, 5.2, 8.4, 4.9, 9.1 New sale revenue (mil. of dollars) - 7.5, 6.9, 8.2, 6.4, 9.3 Let be the mean of old sale revenues and be the mean of new sale revenues, both in millions of dollars per month.
(a) At the level of significance = 0.09, test H: versus H: < .
(b) Interpret your results in part (a).
(c) Find the pvalue for the test in part (a). Would you reject H if = 0.05?
(d) Construct the 91% confidence interval for mean of the difference between before and afteradvertising sale revenues.
Explanation / Answer
a)
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
At level of significance = 0.09
As we can see, this is a right tailed test.
Calculating the standard deviation of the differences (third column):
s = 0.624984848
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.279501721
Calculating the mean of the differences (third column):
XD = 0.68
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 2.43290094
As df = n - 1 = 4
Then the critical value of t is
tcrit = + 1.622577966
As t > 1.6226, WE REJECT THE NULL HYPOTHESIS. [ANSWER]
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b)
Hence, there is significant evidence at 0.09 level that the mean of new sale revenues is greater than the mean of old sale revenues. [CONCLUSION]
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c)
Also, using technology to get p value,
p = 0.035877941
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.
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d)
For the 0.91 confidence level,
alpha/2 = (1 - confidence level)/2 = 0.045
t(alpha/2) = 2.226099557
lower bound = [X1 - X2] - t(alpha/2) * sD = 0.057801342
upper bound = [X1 - X2] + t(alpha/2) * sD = 1.302198658
Thus, the confidence interval is
( 0.057801342 , 1.302198658 ) [ANSWER]
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