uestion 1: What is the value m in the table below, if the mean and the variance of the random variable X are μ x = 25 and σ 2 x = 80? X 1 0 2 0 3 0 3 5 m Probabi lity . 1 . 5 . 1 . 2 . 1 m = 30 m = 35 m = 38 m = 40 m = 45 Question 2: Two distributions D 1 and D 2 are displayed on the same graph. If the distribution D 1 is right skewed, the distribution D 2 is left skewed, and the mean of D 1 is lower than the mean of D 2 , which of the following statements is not true? The median of D 1 is lower than the median of D 2 The mean of D 1 is lower than the median of D 2 . The mean of D 2 is lower than the median of D 1 . The median of D 1 is lower than the mean of D 2 . The mean of D 2 is lower than the median of D 2 . Question 3: A large sample of size n is used to estimate
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
uestion 1: What is the value m in the table below, if the mean and the variance of the random variable X are μx = 25 and σ2
x = 80? X 10 20 30 35 m
Probability .1 .5 .1 .2 .1
m = 30
m = 35
m = 38
m = 40
m = 45
Question 2: Two distributions D1 and D2 are displayed on the same graph. If the distribution D1 is right skewed, the distribution D2 is left skewed, and the mean of D1 is lower than the mean of D2, which of the following statements is not true?
The median of D1 is lower than the median of D2
The mean of D1 is lower than the median of D2.
The mean of D2 is lower than the median of D1.
The median of D1 is lower than the mean of D2.
The mean of D2 is lower than the median of D2.
Question 3: A large sample of size n is used to estimate the confidence interval for a proportion p. After further evaluation, the standard deviation of the sample distribution is considered too large. What size sample do we need to use for a new standard error equal to one tenth of the original standard error?
10n
50n
100n
141n
200n
Question 4: A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. What is the probability that both marbles are red?
1/50
1/60
1/66
1/24
1/18
Question 5: A large automobile manufacturer states that approximately 4% of all their cars made in 2010 have a defective component. Two samples of 150 cars (sample A) and 250 cars (sample B) were taken to test for the defective component. Which of the following statements must be true:
mean of sample A < mean of sample B
mean of the sample A > mean of sample B
standard deviation of sample A = standard deviation of sample B
standard deviation of sample A < standard deviation of sample B
standard deviation of sample A > standard deviation of sample B
Question 6: You roll a die until you get a 5 or a 6. What is the variance of this distribution?
6
3
1/3
8
12
Question 7: A back to back stem and leaf plot compares the heights of the players of two basketball teams. All heights in the plot below are in inches.
Team A Team B
6 8 9
1 4 4 4 5 8 9 7 2 3 6 6 6 8 9
1 1 2 4 8 2 5 6
The means of the two distributions are the same.
The medians of the two distributions are the same.
The ranges of the two distributions are the same.
The distributions have the same number of observations.
None of the statements above is correct.
Question 8: A car manufacturer wishes to estimate the difference in early failures between cars sold in a warm climate and cars sold in a cold climate. They take a random sample of 500 cars from each group. The means obtained are 4.1 failures for cars running in a warm climate and 3.8 failures for cars running in a cold climate. The standard deviation for both populations is 0.4 failures. Find the 95% confidence interval for the difference in the population means.
0.3 +/- 0.0333
0.3 +/- 0.0350
0.3 +/- 0.0400
0.3 +/- 0.0452
0.3 +/- 0.0496
Question 9: A nutritional consulting company is trying to find what percentage of the population of a town is overweight. The marketing department of the company contacts by telephone 600 people from a list of the entire town's population. All 100 people give answers to the survey. Which of the following is the most significant source of bias in this survey?
Size of sample.
Undercoverage.
Voluntary response bias
Nonresponse.
Response bias.
Question 10: Which of the following are true statements: I. All bell-shaped distributions are symmetric. II. Bar charts are useful to describe quantitative data.III. Cumulative frequency plots are useful to describe quantitative data.
I only.
I and II only.
II and III only.
I and III only.
I, II and III.
Question 11: A random sample of 400 passengers of an airline is polled after their flights. Of the passengers, 300 say they will fly again with the same airline. Which of the following is a 90% confidence interval for the proportion of passengers that will fly again with the same airline?
0.75 +/- 0.066
0.75 +/- 0.005
0.75 +/- 0.045
0.75 +/- 0.036
0.75 +/- 0.15
Question 12: The mean number of points per game scored by basketball players during a high school championship is 9.4, and the standard deviation is 1.5. Assuming that the number of points are normally distributed, what number of points per game will place a player in the top 15% players taking part in the basketball championship?
9.10 points per game
10.57 points per game
10.95 points per game
12.35 points per game
13.96 points per game
Question 13: A residual plot:
displays residuals of the response variable versus the independent variable.
displays residuals of the independent variable versus the response variable
displays residuals of the independent variable versus residuals of the response variable.
displays the independent variable versus the response variable.
displays the response variable versus the dependent variable.
Question 14: For any A and B random variables, which of the following statements must be true: I: μA+B = μA + μB
II σ2A-B = σ2
A + σ2B
III σ2A+B = σ2
A - σ2B
I only.
II only.
I and II.
II and II.
I and II and II.
Question 15: A random sample of 1000 balances in the retirement accounts of exempt employees of a company has a sample mean of μ1 = $100,000 and a standard deviation σ1 = $12,000. A random sample of 4000 balances in the retirement accounts of hourly employees of the same company has a sample mean of μ2 = $80,000 and a standard deviation σ2 = $14,000. If X is the sampling distribution of the differences in account balances of the two categories of employees, what is σx?
$439.3
$2657.6
$5490.9
$11,065
$13,000
Question 16: Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is equally likely to pick any of the eight ice cream flavors. What is the probability that each child orders a different ice cream type?
5/72
2/5
7/64
105/256
45/128
Question 17: The rainfall of a county is measured for 14 years in a row to ascertain the local corn crop. No irrigation was used during this time.Variable Coefficient s.e. of coefficient
Constant 33 .8
Rainfall 1.45 .422
Find the 96% confidence interval for the slope of the least squares regression line.
1.45 +/- .056
1.45 +/- .972
1.45 +/- 1.1
33 +/- .972
33 +/- .645
Question 18: An electronics company designs and manufactures DC voltage power supplies. The output voltages of the power supplies have accuracy errors that are caused by three independent internal circuits: A, B and C. Past measurements have shown that circuit A creates an error with a mean of 100mV and a standard deviation of 20mV, circuit B creates an error with a mean of 80mV and a standard deviation of 10mV and circuit C creates an error with a mean of 50mV and a standard deviation of 10mV. What is the standard deviation of the error of the power supplies caused by all three circuits?
12mV
24.5mV
32.5mV
40mV
55mV
Question 19: An opinion survey will be conducted at three corporations. Corporation A has 40,000 employees, corporation B has 60,000 employees and corporation C has 125,000 employees. The results of each survey will be used to estimate the opinions of employees at each corporation. Each survey will be conducted with a simple random sample of 500 employees. Which corporation will have its employees opinions estimated more accurately by the surveys?
Corporation A.
Corporation B.
Neither corporation will have a more accurate estimate.
Corporation C.
Corporations A and B.
Question 20: The quality department of an electronics manufacturer randomly selected 100 resistors. The mean resistance of the resistors was 201.5Ω and the standard deviation was .4Ω. Find the 98% confidence interval for this problem.
201.5+/-.093
201.5+/-.125
201.5+/-.133
201.5+/-.155
201.5+/-.212
Question 21: The heights of 100 students are normally distributed with a mean of 172cm. What is the standard deviation of the heights given that the probability of a height above 180cm is .25?
7.9cm
8.7cm
9.9cm
10.5cm
11.9cm
Question 22: Six hundreds travelers have purchased airline tickets through the same travel agency. The following table gives the two-way classification of their destination choices. What is the joint relative conditional frequency for female travelers to Asia if the marginal row totals are fixed?
Male Female Totals
Europe 189 195 384
Asia 49 62 111
South America 55 50 105
Totals 293 307 600
a) 53%
b) 56%
c) 58%
d) 61%
e) 63%
Question 23: Out of the 500 students of a school, 30% wear glasses. If we use a simple random sample of 25 students, which of the following statements is correct:
The sampling distribution is small relative to the population.
The sampling distribution is a skewed distribution.
The sampling distribution is normal.
The mean of the sampling distribution is equal to .3.
None of the above.
Question 24: The mean of the weights of a group of 100 men and women is 160lb. If the number of men in the group is 60 and the mean weight of the men is 180lb, what is the mean weight of the women?
a) 120lb
b) 125lb
c) 130lb
d) 132lb
e) 135lb
Question 25: A real estate agent finds home buyers and closes the sales for 70% of his clients that sell thier houses. What is the mean number of sales for his next 10 clients and what is the standard deviation of this distribution?
mean = 7 and standard deviation = 1.45
mean = 7 and standard deviation = 2.5
mean = 10 and standard deviation = 1.45
mean = 10 and standard deviation = 2.5
mean = 7 and standard deviation = 1.33
Question 26: The height and the weight of 18 students were measured and a scatterplot of the measures is shown below. If two pairs of measurements need to be removed from the set of 18, which of the choices shown below decreases the coefficient of correlation the most?
a) S2 and S3
b) S2 and S5
c) S1 and S3
d) S2 and S4
e) S1 and S2
Question 27: It takes different times for different workers to perform the same specific task, as it is shown in the distribution below. The boxplot displays time in minutes. Which of the following statements must be true?
a) The 25th percentile is greater than 70 minutes.
b) The distribution is skewed to the left.
c) The interquartile range is higher than 20 minutes.
d) distribution median < distribution mean
e) distribution median = distribution mean
Question 28: Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?
.32
.4
.46
.5
.58
Question 29: A pharmaceutical company claims that its weight loss drug allows women to lose 8.5lb after one month of treatment. If we want to conduct an experiment to determine if the patients are losing less weight than advertised, which of the following hypotheses should be used?
H0: μ = 8.5; Ha: μ > 8.5
H0: μ = 8.5; Ha: μ ≠ 8.5
H0: μ = 8.5; Ha: μ < 8.5
H0: μ ≠ 8.5; Ha: μ < 8.5
H0: μ ≠ 8.5; Ha: μ > 8.5
Question 30: A car manufacturer claims that 90% of their cars do not experience engine failures before reaching a mileage of 150,000 miles. A sample of 65 cars is investigated and 9 of the cars had an engine failure before 150,000 miles. Which of the following is an appropriate test outcome?
z = 0.552 p = .214
z = -0.274 p = .214
z = -0.274 p = .151
z = -1.034 p = .214
z = -1.034 p = .151
Question 31: A tutoring company tests the results of their intensive training for a standardized test. Six students randomly selected have taken the test before and after having been trained by the company. The following table gives the test scores of the 6 students:Before 88 79 77 83 69
After 78 54 83 73 71
The appropriate test for this situation is:
a matched pair t-test
a chi-square goodness of fit test
a two-sample z-test
a one-sample t-test
a one-sample z-test
Question 32: The Department of Transportation of the State of New York claimed that it takes an average of 200 minutes to travel by train from New York to Buffalo. A random sample of 40 trains was taken and the average time required to travel from New York to Buffalo was 188 minutes, with a standard deviation of 28 minutes. What is the p-value for this test?
.0355
.0099
.1294
.2881
.1167
m = 40
Not answered
2 the mean of D2 is lower than the median of D1.Not answered
3 100nNot answered
4 1/66Not answered
5standard deviation of sample A > standard deviation of sample B
Not answered
6 6Not answered
7 None of the statements above is correct.Not answered
8 0.3 +/- 0.0496Not answered
9 Response bias.Not answered
10 I and III only.Not answered
11 0.75 +/- 0.036Not answered
12 10.95 points per gameNot answered
13displays residuals of the response variable versus the independent variable.
Not answered
14 I onlyNot answered
15 $439.3Not answered
16 105/256Not answered
17 1.45 +/- .972Not answered
18 24.5mVNot answered
19 Neither corporation will have a more accurate estimate. Not
answered
20 201.5+/-.093Not answered
21 11.9cmNot answered
22 56%Not answered
23 The sampling distribution is a skewed distribution.Not answered
24 130lbNot answered
25 mean = 7 and standard deviation = 1.45Not answered
26 S2 and S4Not answered
27 The distribution is skewed to the left.Not answered
28 .58Not answered
29 H0: mu = 8.5; Ha: mu < 8.5Not answered
30 z = -1.034 p = .151Not answered
31 a matched pair t-testNot answered
32 .0099
roblem 1
Which of the following statements are true? (Check one)
I. Categorical variables are the same as qualitative variables.
II. Categorical variables are the same as quantitative variables.
III. Quantitative variables can be continuous variables.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Solution
The correct answer is (E). Categorical variables are just another name for qualitative
variables. And quantitative variables are numeric variables, so they can be continuous
variables. Categorical variables, however, are not quantitative variables.
See
also:
Variabl
es
Problem 2
A coin is tossed three times. What is the probability that it lands on heads exactly one time?
(A) 0.125
(B) 0.250
(C) 0.333
(D) 0.375
(E) 0.500
Solution
The correct answer is (D). If you toss a coin three times, there are a total of eight possible
outcomes. They are: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. Of the eight possible
outcomes, three have exactly one head. They are: HTT, THT, and TTH. Therefore, the
probability that three flips of a coin will produce exactly one head is 3/8 or 0.375.
See
also:
Probabilit
y
Problem 3
An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car
buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and
2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling
100 buyers of each brand.
Is this an example of a simple random sample?
(A) Yes, because each buyer in the sample was randomly sampled.
(B) Yes, because each buyer in the sample had an equal chance of being sampled.
(C) Yes, because car buyers of every brand were equally represented in the sample.
(D) No, because every possible 400-buyer sample did not have an equal chance of
being chosen.
(E) No, because the population consisted of purchasers of four different brands of car.
Solution
The correct answer is (D). A simple random sample requires that every sample of size n (in
this problem, n is equal to 400) have an equal chance of being selected. In this problem,
there was a 100 percent chance that the sample would include 100 purchasers of each
brand of car. There was zero percent chance that the sample would include, for example, 99
Ford buyers, 101 Honda buyers, 100 Toyota buyers, and 100 GM buyers. Thus, all possible
samples of size 400 did not have an equal chance of being selected; so this cannot be a
simple random sample.
The fact that each buyer in the sample was randomly sampled is a necessary condition for a
simple random sample, but it is not sufficient. Similarly, the fact that each buyer in the
sample had an equal chance of being selected is characteristic of a simple random sample,
but it is not sufficient. The sampling method in this problem used random sampling and
gave each buyer an equal chance of being selected; but the sampling method was
actually stratified random sampling.
The fact that car buyers of every brand were equally represented in the sample is irrelevant
to whether the sampling method was simple random sampling. Similarly, the fact that
population consisted of buyers of different car brands is irrelevant.
See
also:
Survey Sampling
Methods
Problem 4
Which of the following statements is true?
I. The center of a confidence interval is a population parameter.
II. The bigger the margin of error, the smaller the confidence interval.
III. The confidence interval is a type of point estimate.
IV. A population mean is an example of a point estimate.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) None of the above.
Solution
The correct answer is (E). The center of a confidence interval is a sample statistic, not a
population parameter. The confidence interval is equal to the sample statistic plus or minus
the margin of error; so the confidence interval gets bigger as the margin of error gets
bigger. A confidence interval is a type of interval estimate, not a type of point estimate.
A population mean is not an example of a point estimate; a sample mean is an example of a
point estimate.
See
also:
Estimation
Problems
Problem 5
A sample consists of four observations: {1, 3, 5, 7}. What is the standard deviation?
(A) 2
(B) 2.58
(C) 6
(D) 6.67
(E) None of the above
Solution
The correct answer is (B). First, we need to compute the sample mean.
x = ( 1 + 3 + 5 + 7 ) / 4 = 4
Then, we plug all of the known values into the formula for the standard deviation of a