Instructions:
1) Show your work. For calculator problems, record the command(s) youused.
2) Do your calculations using formulas unless otherwiseindicated.
3) You may assume that all samples are simple randomsamples.
1. The beverages ordered by a sample of customers at a restaurant is given in thechart.
|
Beverage
|
Pop Beer Wine Coffee Tea
|
|
Number
|
31 8 10 25 6
|
a. Find the test statistic you would use to test the claim that the different beverage types areordered with the samefrequency.
b. With .05 significance, test the claim that the proportion of orders of pop, beer, wine, coffee andtea are .40, .10, .10, .20 and .20, respectively. Useformula/chart.
2. The credit scores for a sample of residents in 3 different suburbs is given in thetable.
|
SuburbA
|
312 325 336 400 720 738 801 813
|
|
SuburbB
|
630 655 683 692 702 712 715 726 728 732 733
|
|
SuburbC
|
519 528 543 740 752 783 791 802
|
a. Use your calculator to test the claim that the mean credit score for all three suburbs is thesame.
Use .10 significance. You may assume that the population distributions are approximatelynormal.
b. With .05 significance, test the claim that the median credit score in suburb B is 655. Use theSign Test.
3. A sample of college students took a math test. The grade and amount of sleep had the previousnight are recorded in thetable.
|
A
|
B
|
C
|
D
|
F
|
|
Less than 7 Hours ofSleep
|
3
|
6
|
17
|
15
|
10
|
|
7 or More Hours ofSleep
|
10
|
25
|
32
|
6
|
2
|
a. Calculate the expected value of the cell with less than 7 hours of sleep and an "A" on the exam.Use aformula.
b. Use your calculator to test the claim that sleep and test grade are independent with .05significance.
4. The monthly savings amount for a sample of people before and after attending a financialplanning seminar in given in thechart.
|
Before
|
500 815 625 0 1050 160 35 230 980
|
|
After
|
550 750 610 25 1050 210 50 240 930
|
Use the Wilcoxon Signed-Ranks test to test the claim that the matched pairs have differences thatcome from a population with a median equal to zero. Use .05significance.
5. In a sample of 8 houses in a subdivision, 2 have holiday decorationsdisplayed.
a. With .05 significance, test the claim that fewer than half of the houses in the subdivisionhave holiday decorationsdisplayed.
b. Why can't we use the hypothesis test described in section 8-3 for thisproblem?
c. With .05 significance, test the claim that more than half of the houses in the subdivision haveholiday decorations displayed. (Hint: Read pages 639 and 640 in your book verycarefully.)
d. Find the test statistic (from chapter 13) you would use to test the claim that fewer than half ofthe houses have decorations if there are 15 houses with decorations in a sample of 41 houses. Donot perform thetest.