In: Statistics and Probability
(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
(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.