In: Statistics and Probability
2. To raise awareness of its capabilities, FedEx developed a sales promotion that was sent to selected offices. To assess the possible benefit of the promotion, FedEx pulled the shipping records for a random sample of 50 offices that received the promotion and another random sample of 75 that did not and collected data on the number of mailings. They want to see if those who received the sales promotions shipped more mailings. The complete set of results is provided below (promotions columns). a. State the null and alternate hypotheses. b. Run the test. Paste the test output and state your decision (minitab - Stat-paired T-Test and CI). c. What is the best estimate for the population difference in means for the number of mailings between offices with the promotion and offices without the promotion? (Be 90% confident in your estimate for the confidence interval). d. Interpret the confidence interval in part c. e. What is the margin of error associated with 90% confidence interval?
Promotion Mailings
Promotions_NO 15
Promotions_NO 49
Promotions_NO 42
Promotions_NO 22
Promotions_NO 26
Promotions_NO 35
Promotions_NO 38
Promotions_NO 13
Promotions_NO 35
Promotions_NO 14
Promotions_NO 5
Promotions_NO 64
Promotions_NO 27
Promotions_NO 57
Promotions_NO 50
Promotions_NO 43
Promotions_NO 32
Promotions_NO 39
Promotions_NO 13
Promotions_NO 19
Promotions_NO 47
Promotions_NO 45
Promotions_NO 38
Promotions_NO 59
Promotions_NO 35
Promotions_NO 8
Promotions_NO 10
Promotions_NO 58
Promotions_NO 44
Promotions_NO 9
Promotions_NO 10
Promotions_NO 0
Promotions_NO 42
Promotions_NO 37
Promotions_NO 23
Promotions_NO 12
Promotions_NO 54
Promotions_NO 41
Promotions_NO 36
Promotions_NO 43
Promotions_NO 45
Promotions_NO 18
Promotions_NO 65
Promotions_NO 10
Promotions_NO 17
Promotions_NO 59
Promotions_NO 26
Promotions_NO 18
Promotions_NO 8
Promotions_NO 14
Promotions_NO 74
Promotions_NO 29
Promotions_NO 60
Promotions_NO 19
Promotions_NO 30
Promotions_NO 29
Promotions_NO 12
Promotions_NO 0
Promotions_NO 20
Promotions_NO 31
Promotions_NO 13
Promotions_NO 5
Promotions_NO 7
Promotions_NO 42
Promotions_NO 36
Promotions_NO 9
Promotions_NO 23
Promotions_NO 70
Promotions_NO 28
Promotions_NO 25
Promotions_NO 26
Promotions_NO 24
Promotions_NO 50
Promotions_NO 7
Promotions_NO 0
Promotions_YES 38
Promotions_YES 74
Promotions_YES 18
Promotions_YES 65
Promotions_YES 60
Promotions_YES 51
Promotions_YES 71
Promotions_YES 47
Promotions_YES 29
Promotions_YES 39
Promotions_YES 45
Promotions_YES 36
Promotions_YES 57
Promotions_YES 36
Promotions_YES 12
Promotions_YES 20
Promotions_YES 23
Promotions_YES 79
Promotions_YES 16
Promotions_YES 4
Promotions_YES 62
Promotions_YES 37
Promotions_YES 2
Promotions_YES 23
Promotions_YES 6
Promotions_YES 10
Promotions_YES 28
Promotions_YES 65
Promotions_YES 25
Promotions_YES 86
Promotions_YES 27
Promotions_YES 58
Promotions_YES 33
Promotions_YES 54
Promotions_YES 40
Promotions_YES 92
Promotions_YES 71
Promotions_YES 0
Promotions_YES 77
Promotions_YES 60
Promotions_YES 56
Promotions_YES 38
Promotions_YES 16
Promotions_YES 89
Promotions_YES 62
Promotions_YES 9
Promotions_YES 42
Promotions_YES 73
Promotions_YES 49
Promotions_YES 14
MINITAB used:
To raise awareness of its capabilities, FedEx developed a sales promotion that was sent to selected offices. To assess the possible benefit of the promotion, FedEx pulled the shipping records for a random sample of 50 offices that received the promotion and another random sample of 75 that did not and collected data on the number of mailings. They want to see if those who received the sales promotions shipped more mailings. The complete set of results is provided below (promotions columns).
a. State the null and alternate hypotheses.
Group1 : Promotions_YES
Group2 : Promotions_NO
Ho: µ1 = µ2 H1: µ1 > µ2
b. Run the test. Paste the test output and state your decision (minitab - Stat-paired T-Test and CI).
There are two different groups, independent sample t test used.
Two-Sample T-Test and CI: Promotions_YES, Promotions_NO
Method
μ₁: mean of Promotions_YES |
µ₂: mean of Promotions_NO |
Difference: μ₁ - µ₂ |
Equal variances are assumed for this analysis.
Descriptive Statistics
Sample |
N |
Mean |
StDev |
SE Mean |
Promotions_YES |
50 |
42.5 |
25.0 |
3.5 |
Promotions_NO |
75 |
29.8 |
18.5 |
2.1 |
Estimation for Difference
Difference |
Pooled |
90% Lower Bound |
12.64 |
21.32 |
7.63 |
Test
Null hypothesis |
H₀: μ₁ - µ₂ = 0 |
Alternative hypothesis |
H₁: μ₁ - µ₂ > 0 |
T-Value |
DF |
P-Value |
3.25 |
123 |
0.001 |
Calculated t= 3.25, P=0.001 which is < 0.10 level of significance. Ho is rejected.
We conclude that those who received the sales promotions shipped more mailings.
c. What is the best estimate for the population difference in means for the number of mailings between offices with the promotion and offices without the promotion? (Be 90% confident in your estimate for the confidence interval).
best estimate for the population difference in means = 12.64
Estimation for Difference
Difference |
Pooled |
90% CI for |
12.64 |
21.32 |
(6.19, 19.09) |
90% CI for mean difference = (6.19, 19.09)
d. Interpret the confidence interval in part c.
we are 90% confident that the population difference in means for the number of mailings between offices with the promotion and offices without the promotion falls in the interval (6.19, 19.09).
e. What is the margin of error associated with 90%
margin of error = (19.09-6.19)/2 = 6.45