Deck 7: Sampling Distributions and Sampling

Question 1

Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

A) 0.7357
B) approximately 0
C) approximately 1
D) 0.2357

Answer 1

C

Question 2

Why is the Central Limit Theorem so important to the study of sampling distributions?

A) It allows us to disregard the size of the population we are sampling from.
B) It allows us to disregard the size of the sample selected when the population is not normal.
C) It allows us to disregard the shape of the population when n is large.
D) It allows us to disregard the shape of the sampling distribution when the size of the population is large.

Answer 2

C

Question 3

Which of the following sampling methods will more likely be susceptible to ethical violation when used to form conclusions about the entire population?

A) simple random sample
B) judgement sample
C) cluster sample
D) stratified sample

Answer 3

B

Question 4

TABLE 7-5
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.
Referring to Table 7-5, the manager decides to ask a sample of customers, who have bought a videocassette recorder made by the company and filed a complaint over the past year, to fill in a survey about whether they are satisfied with the product. This method will most likely suffer from

A) non-probability sampling.
B) coverage error.
C) measurement error.
D) non-response error.

Question 5

Which of the following is true about the sampling distribution of the sample mean?

A) The shape of the sampling distribution is always approximately normal.
B) The mean of the sampling distribution is always µ.
C) The standard deviation of the sampling distribution is always ?.
D) All of the above are true.

Question 6

The standard error of the population proportion will become larger

A) as population proportion approaches 1.00.
B) as the sample size increases.
C) as population proportion approaches 0.50.
D) as population proportion approaches 0.

Question 7

Which of the following statements about the sampling distribution of the sample mean is incorrect?

A) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.
B) The mean of the sampling distribution of the sample mean is equal to µ.
C) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n c 30).
D) The standard deviation of the sampling distribution of the sample mean is equal to a.

Question 8

The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

A) increase the sample size to 400.
B) decrease the sample size to 50.
C) decrease the sample to 25.
D) increase the sample size to 200.

Question 9

Which of the following sampling methods is a probability sample?

A) quota sample
B) chunk
C) stratified sample
D) judgment sample

Question 10

Which of the following sampling methods will more likely be susceptible to ethical violation?

A) cluster sample
B) simple random sample
C) stratified sample
D) convenience sample

Question 11

Which of the following is not a reason for the need for sampling?

A) It is usually too time consuming to look at the whole population.
B) It is sometimes destructive to observe the entire population.
C) It is usually too costly to study the whole population.
D) It is always more informative by investigating a sample than the entire population.

Question 12

Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

A) The mean of the sampling distribution is equal to 23 years.
B) The shape of the sampling distribution is approximately normal.
C) The standard error of the sampling distribution is equal to 0.3 years.
D) The standard deviation of the sampling distribution is equal to 3 years.

Question 13

The use of the finite population correction factor when sampling without replacement from finite populations will

A) reduce the standard error of the mean.
B) not affect the standard error of the mean.
C) only affect the proportion, not the mean.
D) increase the standard error of the mean.

Question 14

The Central Limit Theorem is important in statistics because

A) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
B) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
C) for a large n, it says the population is approximately normal.
D) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Question 15

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

A) 67%
B) 16%
C) 29%
D) 84%

Question 16

For sample size 1, the sampling distribution of the mean will be normally distributed

A) regardless of the shape of the population.
B) only if the population is normally distributed.
C) only if the shape of the population is symmetrical.
D) only if the population values are positive.

Question 17

Sales prices of baseball cards from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.

A) normal with a mean of $5.25 and a standard error of $2.80
B) skewed-right with a mean of $5.25 and a standard error of $2.80
C) normal with a mean of $5.25 and a standard error of $0.28
D) skewed-right with a mean of $5.25 and a standard error of $0.28

Question 18

A telemarketer set the company's computerized dialing system to contact every 25th person listed in the local telephone directory. What sampling method was used?

A) stratified sample
B) cluster sample
C) systematic sample
D) simple random sample

Question 19

A sample of 300 subscribers to a particular magazine is selected from a population frame of 9,000 subscribers. If, upon examining the data, it is determined that no subscriber had been selected in the sample more than once

A) the sample had to have been selected without replacement.
B) the sample could not have been random.
C) the sample had to have been selected with replacement.
D) the sample may have been selected without replacement or with replacement.

Question 20

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

A) 0.050
B) 0.800
C) 0.003
D) 0.200

Question 21

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

A) 18.750
B) 1.875
C) 0.750
D) 2.500

Question 22

For sample size 16, the sampling distribution of the mean will be approximately normally distributed

A) if the sample is normally distributed.
B) if the shape of the population is symmetrical.
C) regardless of the shape of the population.
D) if the sample standard deviation is known.

Question 23

Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with µ = 6 ounces and a = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

A) The shape of the sample distribution is approximately normal.
B) The mean of the sampling distribution is 6 ounces.
C) The standard deviation of the sampling distribution is 2.5 ounces.
D) All of the above are correct.

Question 24

For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed

A) only if the population is normally distributed.
B) only if the shape of the population is symmetrical.
C) only if the standard deviation of the samples are known.
D) regardless of the shape of the population.

Question 25

A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain?

A) 3
B) 5
C) 6
D) 4

Question 26

Which of the following sampling methods will more likely be susceptible to ethical violation when used to form conclusions about the entire population?

A) convenient sample
B) systematic sample
C) simple random sample
D) cluster sample

Question 27

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

A) 0.029
B) 0.050
C) 0.120
D) 0.091

Question 28

TABLE 7-5
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.
Referring to Table 7-5, if there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a

A) systematic sample.
B) cluster sample.
C) stratified sample.
D) simple random sample.

Question 29

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

A) minimum variance.
B) random.
C) biased.
D) unbiased.

Question 30

Since a ______is not a randomly selected probability sample, there is no way to know how well it represents the overall population.

A) stratified sample
B) simple random sample
C) cluster sample
D) quota sample

Question 31

The standard error of the mean

A) decreases as the sample size increases.
B) measures the variability of the mean from sample to sample.
C) is never larger than the standard deviation of the population.
D) all of the above

Question 32

A population frame for a survey contains a listing of 6,179 names. Using a table of random numbers, which of the following code numbers will appear on your list?

A) 6946
B) 06
C) 0694
D) 61790

Question 33

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

A) It has a normal distribution with the same mean and standard deviation as the population.
B) It has a normal distribution with the same mean as the population but with a smaller standard deviation.
C) It has the same shape and mean as the population, but has a smaller standard deviation.
D) It has the same shape, mean, and standard deviation as the population.

Question 34

Which of the following can be reduced by proper interviewer training?

A) sampling error
B) measurement error
C) both of the above
D) none of the above

Question 35

TABLE 7-2
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken.
Referring to Table 7-2, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie?

A) $116,000- $118,000
B) $114,000- $116,000
C) $113,000- $115,000
D) $115,000- $117,000

Question 36

TABLE 7-5
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.
Referring to Table 7-5, which of the following questions in the survey will not likely induce a measurement error?

A) How many times have you failed to set the time on the videocassette recorder?
B) How many times have you brought the videocassette recorder back for service?
C) How many times have you illegally copied copyrighted sporting events?
D) What is your exact annual income?

Question 37

Which of the following types of samples can you use if you want to make valid statistical inferences from a sample to a population?

A) a quota sample
B) a probability sample
C) a judgment sample
D) a chunk

Question 38

The Dean of Students mailed a survey to a total of 400 students. The sample included 100 students randomly selected from each of the freshman, sophomore, junior, and senior classes on campus last term. What sampling method was used?

A) cluster sample
B) simple random sample
C) stratified sample
D) systematic sample

Question 39

For a population frame containing N = 1,007 individuals, what code number should you assign to the first person on the list in order to use a table of random numbers?

A) 0
B) 01
C) 1
D) 0001

Question 40

The evening host of a dinner dance reached into a bowl, mixed all the tickets around, and selected the ticket to award the grand door prize. What sampling method was used?

A) stratified sample
B) simple random sample
C) cluster sample
D) systematic sample

Question 41

TABLE 7-7
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected.

-Referring to Table 7-7, the standard error of all possible sample proportions is _____.

Question 42

TABLE 7-6
According to an article, 19% of the entire U.S. population have high-speed access to the Internet. Random samples of size 200 are selected from the U.S. population.

-Referring to Table 7-6, among all the random samples of size 200, ______ % will have more than 30% who have high-speed access to the Internet.

Question 43

TABLE 7-7
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected.

-Referring to Table 7-7, _____ % of the samples are likely to have less than 37.5% who take advantage of online customer service.

Question 44

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

A) 0.0228
B) 0.0013
C) 0.0001
D) 0.4987

Question 45

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

A) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.
B) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.
C) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.
D) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.

Question 46

TABLE 7-5
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products.
Referring to Table 7-5, if a customer survey questionnaire is included in all the videocassette recorders made and sold by the company over the past 12 months, this method of collecting data will most like suffer from

A) nonresponse error.
B) nonprobability sampling.
C) measurement error.
D) coverage error.

Question 47

TABLE 7-6
According to an article, 19% of the entire U.S. population have high-speed access to the Internet. Random samples of size 200 are selected from the U.S. population.

-Referring to Table 7-6, among all the random samples of size 200, _______ % will have between 14% and 24% who have high-speed access to the Internet.

Question 48

TABLE 7-4
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.

-Referring to Table 7-4, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

Question 49

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. A sample of 25 vitamins is to be selected. So, 95% of all sample means will be greater than how many grams?

Question 50

TABLE 7-4
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.
Referring to Table 7-4, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

Question 51

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is _ .

Question 52

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

Question 53

A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than _____% of minority students.

Question 54

TABLE 7-2
The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken.
Referring to Table 7-2, what is the probability that the sample mean selling price was between $113,000 and $117,000?

Question 55

Sampling distributions describe the distribution of

A) statistics.
B) parameters.
C) both parameters and statistics.
D) neither parameters nor statistics.

Question 56

TABLE 7-6
According to an article, 19% of the entire U.S. population have high-speed access to the Internet. Random samples of size 200 are selected from the U.S. population.

-Referring to Table 7-6, among all the random samples of size 200, 90 _____% will have less than
% who have high-speed access to the Internet.

Question 57

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. A sample of 25 vitamins is to be selected. So, the middle 70% of all sample means will fall between what two values?

Question 58

TABLE 7-7
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected.

-Referring to Table 7-7, 90% of the samples proportions symmetrically around the population proportion will have between _____% and___ % of the customers who take advantage of online customer service.

Question 59

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?

Question 60

Which of the following is not a reason for drawing a sample?

A) A sample is less cumbersome and more practical to administer.
B) A sample is less time consuming than a census.
C) A sample is usually not a good representation of the target population.
D) A sample is less costly to administer than a census.

Question 61

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is_____ .

Question 62

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What would you expect the standard error of the mean to be?

Question 63

Referring to Table 7-4, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is _____ .

Question 64

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. So, 95% of the sample means based on samples of size 64 will be between _____and____ .

Question 65

TABLE 7-1
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.
Referring to Table 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

Question 66

TABLE 7-4
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.
Referring to Table 7-4, 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

Question 67

TABLE 7-3
The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.
Referring to Table 7-3, the probability is 0.15 that the sample mean lifetime is more than how many hours?

Question 68

TABLE 7-6
According to an article, 19% of the entire U.S. population have high-speed access to the Internet. Random samples of size 200 are selected from the U.S. population.

-Referring to Table 7-6, among all the random samples of size 200, 90 % will have more than_______% who have high-speed access to the Internet.

Question 69

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is_____ .

Question 70

TABLE 7-1
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.
Referring to Table 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

Question 71

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

Question 72

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n)_______ sample.

Question 73

TABLE 7-4
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.
Referring to Table 7-4, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

Question 74

A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ______% of minority students.

Question 75

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.

Question 76

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. So, 95% of all sample means will fall between what two values?

Question 77

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is _____minutes.

Question 78

TABLE 7-7
Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected.

-Referring to Table 7-7, _____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service.

Question 79

TABLE 7-3
The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.
Referring to Table 7-3, what is the probability that the sample mean lifetime is more than 1,550 hours?

Question 80

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is _____ .