Question

10a) Do customers spend more after the Promotion than they did before (i.e., their Pre versus Post Promotion spending)? Test this question with all the data, then again with only those people who accepted the offer.

10b Does the market research data match the way people really spend in this database? To answer this question, test whether High/Med High spenders actually spend more than Low/Medium Low spenders on the Pre-Promotion values (you can ignore the Average spenders in this analysis). Perform any follow-up tests as appropriate.

Customer ID	Promotion Offer	Enrolled in Program	Pre Promotion Avg Spend	Post Promotion Avg Spend	Marketing Segment
1	Free Flight Insurance	Yes	150.39	246.32	Average Spender
2	Double Miles + Free Flight Insurance	Yes	90.32	182.8	Low Spender
3	Double Miles	Yes	14.93	20.55	Low Spender
4	Double Miles	Yes	45.86	75.25	Average Spender
5	No Offer	No	257.89	397.05	Med Low Spender
6	Free Flight Insurance	Yes	864.59	1098.3	Med High Spender
7	Double Miles	No	137	94.76	Low Spender
8	No Offer	No	1152.27	781.75	Med High Spender
9	Double Miles	Yes	25.82	144.57	Average Spender
10	Double Miles + Free Flight Insurance	Yes	1540.66	1605.88	High Spender
11	Free Flight Insurance	Yes	253.61	312.15	Average Spender
12	Double Miles + Free Flight Insurance	No	37.4	47.78	Low Spender
13	Free Flight Insurance	Yes	1150.51	806.47	Med High Spender
14	Double Miles + Free Flight Insurance	Yes	22.34	545.82	Average Spender
15	Free Flight Insurance	Yes	179.47	334.25	Average Spender
16	Double Miles	Yes	162.42	678.43	Med Low Spender
17	Double Miles + Free Flight Insurance	Yes	24.85	90.83	Low Spender
18	Double Miles	Yes	285.45	121.53	Med Low Spender
19	Free Flight Insurance	No	3005.15	3012.99	High Spender
20	Double Miles + Free Flight Insurance	Yes	28.81	77.26	Low Spender

Answer 1

Soln

10a)

i)

From the data, we calculate the mean and standard deviation of the two groups.

Mean (X bar) = Sum of Values /n

and

Group 1(Pre-Promotion)

Mean (x₁) = 471.49

Std Dev (s₁) = 749.89

n₁ = 20

Group 2(Post-Promotion)

Mean (x₂) = 533.74

Std Dev (s₂) = 715.01

n₂ = 20

alpha = 0.5

Null and Alternate Hypothesis

H₀: µ₁ = µ₂

H_a: µ₁ < µ₂

Test Statistic

Assuming, the population std deviation is not same.

t = (X_{1 ­­­}– X_{2 ­}– (µ₁ - µ₂))/ (s₁²/n₁ + s₂²/n₂ )^1/2 = -0.27

p-value = TDIST(0.27,20+20-2,1) = 0.39

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis.

Conclusion

There is no difference in pre and post promotion spending of customers

ii)

Considering only those who accepted the offer

Group 1(Pre-Promotion)

Mean (x₁) = 322.67

Std Dev (s₁) = 472.32

n₁ = 15

Group 2(Post-Promotion)

Mean (x₂) = 422.69

Std Dev (s₂) = 452.995

n₂ = 15

alpha = 0.5

Null and Alternate Hypothesis

H₀: µ₁ = µ₂

H_a: µ₁ < µ₂

Test Statistic

Assuming, the population std deviation is not same.

t = (X_{1 ­­­}– X_{2 ­}– (µ₁ - µ₂))/ (s₁²/n₁ + s₂²/n₂ )^1/2 = -0.59

p-value = TDIST(0.59,15+15-2,1) = 0.28

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis.

Conclusion

There is no difference in pre and post promotion spending of customers

b)

Group 1(High Spender & Med High Spender)

Mean (x₁) = 1542.64

Std Dev (s₁) = 852.18

n₁ = 5

Group 2(Low Spender & Med Low Spender)

Mean (x₂) = 115.45

Std Dev (s₂) = 102.71

n₂ = 9

alpha = 0.5

Null and Alternate Hypothesis

H₀: µ₁ = µ₂

H_a: µ₁ > µ₂

Test Statistic

Assuming, the population std deviation is not same.

t = (X_{1 ­­­}– X_{2 ­}– (µ₁ - µ₂))/ (s₁²/n₁ + s₂²/n₂ )^1/2 = 3.73

p-value = TDIST(3.73, 5+9-2,1) = 0.001

Result

Since the p-value is less than 0.05, we reject the null hypothesis.

Conclusion

High/Med High spenders actually spend more than Low/Medium Low spenders on the Pre-Promotion values