Question

In: Statistics and Probability

(2)   The general manager of a regional airline wants to determine how effective their rebate promotions...

(2)   The general manager of a regional airline wants to determine how effective their rebate promotions are. In these campaigns, rebates are valid for one week. To examine their effectiveness, the executive records the daily ticket sales (in $100,000s) during the campaign and during the week after the campaign ends. Test the research hypothesis that sales increase during the campaign at the 5% significance level. a.      What are the null and alternative hypotheses? b.      What is the appropriate p-value? c.       Can they infer at the 5% significance level that sales increase during the campaign? State your conclusion. During After Rebate Week Rebate Week Sales Sales Sunday 28 25 Monday 37 35 Tuesday 23 22 Wednesday 14 13 Thursday 16 18 Friday 45 43 Saturday 15 12

Solutions

Expert Solution

(a)

H0: Null Hypothesis: 0

HA: Alternative Hypothesis: >0

(b)

Day After rebate week (X) Rebate Week (Y) d=X-Y
Sunday 28 25 3
Monday 37 35 2
Tuesday 23 22 1
Wednesday 14 13 1
Thursday 16 18 -2
Fridy 45 43 2
Saturday 15 12 3
Total 10

From the d values, thefollowing statistics are calculated:

n = 7

= 10/7 = 1.4286

sd = 1.7182

SE = sd/

= 1.7182/ = 0.6494

Test statistic is:

t = /SE

= 1.4286/0.6494 = 2.1999

ndf = 7 -1 =6

One Tail - Right Side Test

By Technology, p- value = 0.0351

(c)

Since p-value is less than , the difference is significant. Reject null hypothesis.

Conclusion:

They can infer at the 5% sigificant level that sales increase during the campaign.


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