Question 203799This question is from textbook Introduction to Business Statistics
: Hi Please help me with this problem. It is really hard and I'm not sure if I should be using a z-test or a t-test. Thanks for helping.
Reports say that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and teenage appreciation days that feature special bargains for this age group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director's success by surveying a simple random sample of 45 local teens and finding out how much they spend on their most recent shopping visit to the mall. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teen sin this area might be higher than for US teens as a whole. Identify and interpret the p-value for the test. Using the 0.025 level of significance what conclusion do you reach?
Spent
40.33
46.06
37.98
50.81
19.03
59.36
31.81
45.98
45.07
40.94
51.06
52.36
45.68
72.28
37.07
40.57
17.44
55.28
41.26
52.34
8.39
61.54
49.94
59.13
44.99
55.47
42.17
26.79
37.30
56.98
36.51
52.23
46.55
52.06
11.84
57.28
51.73
50.24
66.58
18.39
19.15
37.50
22.17
48.98
40.63
This question is from textbook Introduction to Business Statistics
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Reports say that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and teenage appreciation days that feature special bargains for this age group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director's success by surveying a simple random sample of 45 local teens and finding out how much they spend on their most recent shopping visit to the mall. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teen sin this area might be higher than for US teens as a whole. Identify and interpret the p-value for the test. Using the 0.025 level of significance what conclusion do you reach?
Spent
40.33
46.06
37.98
50.81
19.03
59.36
31.81
45.98
45.07
40.94
51.06
52.36
45.68
72.28
37.07
40.57
17.44
55.28
41.26
52.34
8.39
61.54
49.94
59.13
44.99
55.47
42.17
26.79
37.30
56.98
36.51
52.23
46.55
52.06
11.84
57.28
51.73
50.24
66.58
18.39
19.15
37.50
22.17
48.98
40.63
-------------------
Ho: u = 39
Ha: u > 39
-----------------------
The sample mean is 23.05
The sample standard deviation is 14.54
-----------------------
Use a t-test on means tests.
------------------------
I ran a t-test and got the following results:
Test statistic: t = 1.8685...
p-value = 0.03418 which is greater than alpha = 0.025
------------------------
Conclusion:
Fail to reject Ho.
----------------
Interpretation: 3.418% of test results would provide
stronger evidence for rejecting Ho. Our criteria was
2.5%, so we fail to reject Ho.
======================================================
Cheers,
Stan H.
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