Question

In: Statistics and Probability

2. To raise awareness of its capabilities, FedEx developed a sales promotion that was sent to...

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

Expert Solution

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 StDev	90% Lower Bound for Difference
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 StDev	90% CI for Difference
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

orchestra answered 2 years ago

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