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.

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