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Questions 1-3 are based on the following "POPULATION" data (N = 63):
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19
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89
|
91
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20
|
95
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36
|
63
|
12
|
79
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|
67
|
54
|
61
|
16
|
39
|
39
|
63
|
61
|
42
|
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31
|
84
|
62
|
76
|
40
|
23
|
10
|
16
|
84
|
|
76
|
76
|
63
|
17
|
78
|
14
|
50
|
86
|
65
|
|
79
|
97
|
39
|
85
|
96
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21
|
36
|
70
|
69
|
|
84
|
67
|
21
|
66
|
79
|
87
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31
|
58
|
77
|
|
66
|
68
|
59
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84
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39
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61
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76
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66
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47
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1 If sampling is done without replacement, the number of possible samples of size n = 5 from the above population is __________
a 7,380,289
b 7,028,847
c 6,677,404
d 6,343,534
2 A random sample of size n = 5 is selected. The data in the highlighted cells above are shown below.
x
95
12
84
66
31
The mean and variance of this sample are:
a x¯ = 57.6 s2 = 885.56
b x¯ = 57.6 s2 = 990.64
c x¯ = 57.6 s2 = 1238.30
d x¯ = 58.2 s2 = 1146.82
3 For the sample means computed from the number of random samples determined in question 1, the expected value or mean of sample means is ______.
Use Excel rather than your calculator to do the calculations.
a 60.26
b 59.85
c 58.25
d 57.54
Questions 4-8 are based on the following:
The mean cost of getting a four-year college degree in a certain region of the country is $52,900 with a standard deviation of $8,500. Assume costs are normally distributed.
4 The fraction of costs in this region that fall within ±$4,500 of the mean cost is?
a 0.4038
b 0.3955
c 0.3674
d 0.3293
5 What fraction of sample means from samples of size n = 16 graduates fall within ±$3,000 from the population mean?
a 0.8812
b 0.8414
c 0.8098
d 0.7722
6 In repeated sampling of n = 25 graduates, what fraction of sample means would fall within ±$4,500 from the population mean?
a 0.9566
b 0.9606
c 0.9812
d 0.9920
7 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: x¯1 = ______, x¯2 = ______
a $49,568 $56,232
b $50,266 $55,534
c $51,082 $54,718
d $52,009 $53,791
8 In another region 10% of the x¯ values from samples of size n = 25 are under $49,500 and 10% are over $55,500. From this sampling distribution information we can conclude that the population mean cost of a four-year college degree is μ = _______ and the population standard deviation is σ = ______.
a $52,500 $10,880
b $52,500 $11,719
c $51,500 $9,642
d $51,500 $9,146
Questions 9-11 are based on the following:
The mean annual Medicare spending per enrollee is $11,200 with a standard deviation of $3,100. Answer questions 9-12 based on the sampling distribution of x¯ for randome samples of size n = 85 enrollees.
9 The fraction of sample means falling within ±$500 from the population mean is ______.
a 0.8638
b 0.8288
c 0.7972
d 0.7656
10 95% of all x¯ values from samples of size n = 85 deviate from the population mean of $11,200 by no more than ±$______.
a $370
b $430
c $555
d $659
11 In repeated sampling of n = 85 enrollees, the middle interval which contains the middle 95% of sample mean spending is: x¯1 = ______, x¯2 = ______
a $10,896 $11,504
b $10,541 $11,859
c $10,239 $12,161
d $9,841 $12,559
12 In the previous question, to reduce the margin of error such that the middle 95% of all sample means deviate from the population mean by no more than ±$250, the minimum sample size is ______.
a 708
b 660
c 624
d 591
The following binary data represent the students taking E270, where "1" is for students who are business majors and "0" for other majors.
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1
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1
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1
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1
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0
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0
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1
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1
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0
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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0
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1
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0
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0
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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0
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1
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0
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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0
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0
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0
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1
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0
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1
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1
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0
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0
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1
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1
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1
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0
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0
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1
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0
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1
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1
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1
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0
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1
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1
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0
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1
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1
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1
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1
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1
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1
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0
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0
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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0
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0
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1
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0
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0
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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0
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1
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1
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1
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0
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1
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1
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1
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0
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1
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0
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1
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0
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1
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0
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1
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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0
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1
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0
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1
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0
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1
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0
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0
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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0
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0
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1
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13 If we take repeated samples of size n = 40 from this population of E270 students, the expected value of sample proportions would be ______.
Use Excel!!
a 0.812
b 0.737
c 0.681
d 0.641
Questions 14-17 are based on the following information
Among all adult Indiana residents 83% are high school graduates. Answer questions 13-17 based on the sampling distribution of p¯ for random samples of n = 400 Indiana residents.
14 The fraction of sample proportions obtained from samples of size n = 400 that fall within ±0.04 (4 percentage points) from the population proportion π is _________.
a 0.9266
b 0.9342
c 0.9668
d 0.9826
15 The fraction of sample proportions obtained from samples of size n = 800 that fall within ±0.03 (3 percentage points) from π is _________.
a 0.9762
b 0.9652
c 0.9500
d 0.9266
16 The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained from samples of size n = 500 are: p¯1 = _______, p¯2 = _______
a 0.780 0.880
b 0.787 0.873
c 0.791 0.869
d 0.797 0.863
17 In the previous question, in order the obtain a margin of error of ±0.02 (MOE = 0.02) for the middle interval that contains the middle 95% of all sample proportions, the minimum sample is: n = ______.
a 1422
b 1356
c 1128
d 1064
Questions 18-20 are based on the following information
Just before a mayoral election a local newspaper polls 450 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 52% of the votes in a two-way race.
18 What is the probability that the newspaper's sample will predict defeat of Johnny Comlately?
a 0.2485
b 0.2119
c 0.1977
d 0.1751
19 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from π = 0.52, in either direction, by no more than ______ (or _____ percentage points).
a 0.046 (4.6 percentage points)
b 0.041 (4.1 percentage points)
c 0.037 (3.7 percentage points)
d 0.035 (3.5 percentage points)
20 In order to make the probability of wrongly predicting defeat at most 5%, the minimum number of voters to be included in the sample should be n = ______?
a 944
b 1068
c 1482
d 1679