If sampling is done without replacement, the number of possible samples of size n = 6 from the above population is __
1 If sampling is done without replacement, the number of possible samples of size n = 6 from the above population is __
a 148,426,963
b 156,238,908
c 162,488,464
d 168,988,003
2 A random sample of size n = 6 is selected. The data in the highlighted cells above are shown below.
x
59
112
45
115
50
141
The mean and variance of this sample are:
x̅ s² a 87 2060.5
b 87 1648.4
c 84 2060.5
d 84 1648.4
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 114.90
b 117.30
c 119.70
d 122.10
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 $55,800 with a standard deviation of $8,700. Assume costs are normally distributed.
4 The fraction of costs in this region that fall within ±$5,000 of the mean cost is?
a 0.5284
b 0.5034
c 0.4648
d 0.4314
5 What fraction of sample means from samples of size n = 16 graduates fall within ±$5,000 from the population mean?
a 0.9494
b 0.9590
c 0.9786
d 0.9982
6 In repeated sampling of n = 25 graduates, what fraction of sample means would fall within ±$3,000 from the population mean?
a 0.8963
b 0.9146
c 0.9329
d 0.9515
7 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: x̅₁ = , x̅₂ =
a $52,390 $59,210
b $52,946 $58,654
c $53,573 $58,027
d $53,990 $57,610
8 In another region 10% of the x̅ 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 = _.
µ σ a $53,000 $10,607
b $52,500 $10,607
c $53,000 $11,719
d $52,500 $11,719
Questions 9-12 are based on the following:
The mean annual Medicare spending per enrollee is $11,700 with a standard deviation of $3,250. Answer questions 9-12 based on the sampling distribution of x̅ for random samples of size n = 90 enrollees.
9 The fraction of sample means falling within ±$600 from the population mean is __.
a 0.9356
b 0.9198
c 0.8904
d 0.8530
10 95% of all x̅ values from samples of size n = 90 deviate from the population mean of $11,700 by no more than ±$______.
a $798
b $671
c $562
d $439
11 In repeated sampling of n = 90 enrollees, the middle interval which includes the middle 95% of sample mean spending is: x̅₁ = , x̅₂ =
a $11,029 $12,371
b $11,138 $12,262
c $11,261 $12,139
d $11,323 $12,077
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 710
b 690
c 670
d 650
The following binary data represent the students taking E270, where "1" is for students who are business majors and "0" for other majors.
1 1 1 1 0 0 1 1 0
1 0 1 1 1 1 0 1 1
1 1 1 0 1 0 0 1 1
1 1 1 1 1 0 1 1 1
1 1 1 1 1 1 1 0 1
1 1 0 1 1 1 1 1 1
1 1 1 1 1 1 0 1 0
0 1 1 1 1 1 1 1 1
1 0 0 0 1 0 1 1 0
0 1 1 1 0 0 1 0 1
1 1 0 1 1 0 1 1 1
1 1 1 1 0 1 1 1 0
1 1 1 1 1 1 0 0 1
0 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 0 0 1
1 1 0 1 1 1 0 1 0
1 1 1 1 1 1 0 1 1
1 1 0 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0
1 0 1 0 0 1 1 1 1
1 1 1 1 1 1 0 1 113 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 0.821
b 0.783
c 0.761
d 0.758
Questions 14-17 are based on the following information
Among all adult Indiana residents 85% are high school graduates. Answer questions 14-17 based on the sampling distribution of p̅ for random samples of n = 520 Indiana residents.
14 The fraction of sample proportions obtained from samples of size n = 520 that fall within ±0.04 (4 percentage points) from the population proportion π is _.
a 0.9476
b 0.9742
c 0.9892
d 0.9938
15 The fraction of sample proportions obtained from samples of size n = 750 that fall within ±0.03 (3 percentage points) from π is _.
a 0.9792
b 0.9452
c 0.9232
d 0.8764
16 The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained from samples of size n = 600 are: p̅₁ = , p̅₂ =
a 0.835 0.865
b 0.831 0.869
c 0.821 0.879
d 0.812 0.888
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 1225
b 1245
c 1265
d 1285
Questions 18-20 are based on the following information
Just before a mayoral election a local newspaper polls 420 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 48% of the votes in a two-way race.
18 What is the probability that the newspaper’s sample will predict Johnny Comlately winning the election?
a 0.2709
b 0.2061
c 0.1539
d 0.1251
19 In repeated polling of n = 420 voters, 95% of sample proportions would deviate from π = 0.48, in either direction, by no more than _ (or percentage points).
a 0.055
b 0.048
c 0.042
d 0.034
20 In order to make the probability of wrongly predicting victory at most 5%, the minimum number of voters to be included in the sample should be n = __?
a 1068
b 1482
c 1679
d 1895
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