BANA 2372 - Business Statistics - Chapter 7 - Practice Questions

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Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

$0.12 million

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is _____.

.002

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Refer to Exhibit 7-4. The standard error of the mean equals _____.

.0200

The standard error of the mean equals _____. Refer to Exhibit 7-4 a. .3636 b. .0331 c. .0200 d. 4.000

.0200

A population has a means of 80 and a sd of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is

.0228

A random sample of 150 people was taken from a very large population. 90 of the people in the sample were females. The standard error of the proportion of females is

.0400

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is _____.

.0400

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is:

.0400.

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is _____.

.0495

____ is a property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates

.0495

The finite correction factor should be used in the computation of when n/N is greater than _____.

.05

A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.

.0668

A sample of 400 observations will be taken from a process. the population proportion equals .8. the probability that the sample proportion will be greater than .83 is

.0668

A sample of 400 observations will be taken from an infinite population. The population proportion equals .8. The probability that the sample proportion will be greater than .83 is:

.0668.

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equal .85. The probability that the sample proportion will be between .9115 and .946

.0819

A population has a means of 180 and a sd of 24. a sample of 64 observations will be taken. the probability that the mean from the sample will be between 183 and 186 is

.1359

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is .2. The mean and standard deviation of the distribution of sample proportions are _____.

.2 and .04

Four hundred registered voters were randomly selected and asked whether gun laws should be changed. Three hundred said "yes," and 100 said "no." Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "no" is _____.

.25

The point estimate of the proportion in the population who will respond "no" is _____. Refer to Exhibit 7-2 a. 75 b. .25 c. .75 d. .50

.25

A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____.

.5 and .047

A population of size 1,000 has a proportion of .5. therefore, the proportion and the standard deviation of the sample proportion for sample of size 100 are

.5 and .050

400 registered voters were randomly selected asked whether gun laws should be changed. 300 said yes and 100 said no. The point estimate of the proportion in the population who will respond yes is

.75

The point estimate of the proportion in the population who will respond "yes" is _____. Refer to Exhibit 7-2 a. 300 b. approximately 300 c. .75 d. .25

.75

A sample of 66 observations will be taken from an infinite population. The population proportion equals .12. The probability that the sample proportion will be less than .1768 is:

.92.

A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals .12. The probability that the sample proportion will be less than .1768 is _____.

.9222

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is _____.

.9511

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

0.0151

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million.

0.0228

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be less than 100 grams?

0.0228

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

0.0228

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?

0.0228

At a computer manufacturing company, the actual size of a particular type 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?

0.029

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is _____

0.0400

0.0416 using Excel or 0.0418 using Table E.2

A manufacturer of power tools claims that the mean 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 __________.

0.0548

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, the standard error of the proportion of students in the samples who are minority students is _________.

0.05745

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is

0.1359

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is _____.

0.1359

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. The mean of all the sample proportions of customers who will make a purchase after visiting the web site is _______. The standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________. The requirements for using a normal distribution to approximate a binomial distribution is fulfilled. what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site? What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site? What is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site? 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site? 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

0.15 or 15% 0.05050 True 0.1596 0.5 0.0015 21.47% 8.528% using Excel or 8.536% using Table E.2

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 35.95 and 35.98 oz. is __________.

0.1891

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that more than half of the students in the sample will be minority students

0.1920 using Excel or 0.1922 using Table E.2

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?

0.200

0.2710 using Excel or 0.2736 using Table E.2

The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean exceeds the population mean by more than 2 hours? What is the probability that the sample mean is more than 3 hours below the population mean? What is the probability that the sample mean differs from the population mean by less than 2 hours? What is the probability that the sample mean differs from the population mean by more than 3 hours?

0.3085 0.2266 0.3829 using Excel or 0.3830 using Table E.2 0.4533 using Excel or 0.4532 using Table E.2

Assume that house prices in a neighborhood are normally distributed with a standard deviation of $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?

0.3173 using Excel or 0.3174 using Table E.2

0.3446

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. The population mean of all possible sample proportions is ______. The standard error of all possible sample proportions is ______. ____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service. ____ % of the samples are likely to have less than 37.5% who take advantage of online customer service. 90% of the samples proportions symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service. 95% of the samples proportions symmetrically around the population Proportion will have between _____% and _____% of the customers who take advantage of online customer service.

0.375 or 37.5% 0.0342 53.48 using Excel or 53.46 using Table E.2 50 31.87 and 43.13 30.79 and 44.21

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?

0.4974

0.6554

0.6898

Four hundred registered voters were randomly selected asked whether gun laws should be changed. Three hundred said "yes," and one hundred said "no." Refer to Exhibit 7-2. The point estimate of the proportion in the population who will respond "yes" is

0.75

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that between 30% and 50% of the students in the sample will be minority students.

0.8034 using Excel or 0.8033 using Table E.2

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. What is the probability that the sample mean lifetime is more than 1,550 hours? The probability is 0.15 that the sample mean lifetime is more than how many hours? The probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

0.8413 1,651.82 hours using Excel or 1,652 hours using Table E.2 64.08 hours using Excel or 64 hours using Table E.2

0.8767

0.8849

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

0.9511

0.9545 using Excel or 0.9544 using Table E.2

0.9772

The mean selling price of new homes in a small town 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. What is the probability that the sample mean selling price was more than $110,000? What is the probability that the sample mean selling price was between $113,000 and $117,000? What is the probability that the sample mean selling price was between $114,000 and $116,000? Without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie?

0.9772 0.5763 using Excel or 0.5762 using Table E.2 0.3108 $114,000 -- $116,000

0.9836

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is .3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is _____.

0200

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is _____.

0228

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____.

0819

1.057

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12, respectively. The standard error of the mean is:

1.20.

The point estimate of the population standard deviation is _____. Refer to Exhibit 7-3 a. 2.000 b. 1.291 c. 1.414 d. 1.667

1.414

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

1.4847

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately _____.

1.4847

The point estimate of the population standard deviation is

1.581

The point estimate of the population standard deviation is _____. Refer to Exhibit 7-1 a. 2.500 b. 1.581 c. 2.000 d. 1.414

1.581

The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is _____.

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. So, 95% of all sample means will be greater than how many grams?

101.7757

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. So, the middle 70% of all sample means will fall between what two values?

104.8 and 115.2

We wish to draw a sample of size 5 without replacement from a population of 50 households. Suppose the households were numbered 01 to 50. Using the following line from a random number table, the households selected would be: 1 1 3 6 2 3 5 6 9 2 9 6 2 3 7 9 0 8 4 2 4 6 8 4 3 6 2 7 1 9 6 4 0 4

11, 36, 23, 56, and 92

How many different samples of size 3 (without replacement) can be taken from a finite population of size 10?

120

The following data was collected from a simple random sample from a process (an infinite population) 13,15,14,16,12 The point estimate of the population mean

The point estimate of the population mean _____. Refer to Exhibit 7-1 a. is 5 b. is 14 c. is 4 d. cannot be determined because the population is infinite

A simple random sample of 64 observations was taken from a large population. The population standard deviation is 120. The sample mean was determined to be 320. The standard error of the mean is

A simple random sample of 64 observations was taken from a large population. The population standard deviation is 120. The sample mean was determined to be 320. The standard error of the mean is _____.

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible equals _____.

A simple random sample of 64 observations was taken from a large population. The sample mean and standard deviation were determined to be 320 and 120, respectively. The standard error of the mean is:

15.

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible is equal to:

15.

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible is equal to: 15. 12. 3. 16. A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size

15.

A simple random sample of 64 observations was taken from a large population. The sample mean and standard deviation were determined to be 320 and 120, respectively. The standard error of the mean is: 40. 15. 1.875. 5.

15. 120/sqrt of 64 = 120/8 =15

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21 A point estimate of the population mean is _____.

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 Refer to Exhibit 7-3. The point estimate of the mean of the population is

18.0

The point estimate of the mean of the population is _____. Refer to Exhibit 7-3 a. 18.0 b. 19.6 c. 108 d. 16, since 16 is the smallest value in the sample

18.0

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

180 and 1.74

According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population. The population mean of all the sample proportions is ______. The standard error of all the sample proportions is ______. Among all the random samples of size 200, ______ % will have between 14% and 24% who have high-speed access to the Internet. Among all the random samples of size 200, ______ % will have between 9% and 29% who have high-speed access to the Internet. Among all the random samples of size 200, ______ % will have more than 30% who have high-speed access to the Internet. Among all the random samples of size 200, ______ % will have less than 20% who have high-speed access to the Internet. Among all the random samples of size 200, 90 % will have less than _____% who have high-speed access to the Internet. Among all the random samples of size 200, 90 % will have more than _____% who have high-speed access to the Internet.

19% or 0.19 0.0277 92.85 using Excel or 92.82 using Table E.2 99.97 0.0000 or virtually zero 64.08 using Excel or 64.06 using Table E.2 22.56 using Excel or 22.55 using Table E.2 15.45

Random samples of size 100 are taken from an infinite population whose population proportion is .2. The mean and standard deviation of the sample proportion are:

2 and .04.

2.5 minutes

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?

2.500

In an interval estimation for a proportion of a population, the critical value of z at 99% confidence is:

2.576

The z value for a 99% confidence interval estimation is:

2.58

Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are _____.

20 and 2.5

Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are

200 and 2

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

35.55

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. So, the middle 95% of the sample means based on samples of size 36 will be between __________ and __________.

35.951 and 36.049 ounces

Random sample of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The means and the standard deviation of the sampling distribution of the sample mean are

36 and 1.86

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are _____.

36 and 1.86

The mean and the standard deviation of the sampling distribution of the sample means are _____.

36 and 1.86

The point estimate of the mean content of all bottles is _____. Refer to Exhibit 7-4 a. .2 b. 4 c. 121 d. .02

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. 95% of all sample means will fall between what two values?

40.1 and 49.9 minutes

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. 90% of the sample means will be greater than what value?

41.8 minutes

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. The expected percentage of minority students in their next group of freshmen is _______.

45%

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

49.83

A manufacturer of power tools claims that the mean 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 standard deviation of the sampling distribution of the sample mean is __________ minutes.

A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____.

How many simple random samples of size 5 can be selected from a population of size 8?

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?

67%

A manufacturer of power tools claims that the mean 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, the middle 95% of the sample means based on samples of size 64 will be between __________ and __________.

70.2 and 89.8 minutes

A manufacturer of power tools claims that the mean 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.

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. Which of the following statements is true?

A t distribution should be used because σ is unknown.

The standard error of the mean a) is never larger than the standard deviation of the population. b) decreases as the sample size increases. c) measures the variability of the mean from sample to sample. d) All of the above.

All of the above.

What is the expected value for the sampling distribution of the sample mean?

Always equal to the population mean

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Approximately 0

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was less than $2.5 million.

Approximately 0

The distribution of the number of loaves of bread sold per week by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 weeks has been selected. What is the approximate probability that the mean number of loaves sold in the sampled weeks exceeds 7,895 loaves?

Approximately 0

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 right skewed 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.

Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.

Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen. II. The standard deviations of two different samples from the same population may be the same. III. Statistical inferences can be used to draw conclusions about the populations based on sample data.

II and III

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

It allows us to disregard the shape of the population when n is large.

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

It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Which of these best describes a sampling distribution of a statistic?

It is the distribution of all of the statistics calculated from all possible samples of the same sample size.

Which of the following is a nonprobability sampling technique?

Judgment sampling

Since the sample size is always smaller than the size of the population, the sample mean must a. always be smaller than the population mean b. be larger than the population mean c. be equal to the population mean d. None of the alternative ANSWERS is correct

None of the alternative ANSWERS is correct

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Refer to Exhibit 7-5. Which of the following best describes the form of the sampling distribution of the sample mean for this situation?

None of the answers is correct. -Approximately normal because the sample size is small relative to the population size -Approximately normal because of the central limit theorem -exactly normal

Sales prices of baseball cards from the 1960s are known to possess a right skewed 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.

Normal with a mean of $5.25 and a standard error of $0.28

Which of the following is a point estimator?

Which of the following is(are) point estimator(s)?

Suppose a sample of n = 50 items is selected 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 σ = 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?

The mean of the sampling distribution is 6 ounces.

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

The mean of the sampling distribution is always µ

Suppose the ages of students in Statistics 101 follow a right skewed 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?

The standard deviation of the sampling distribution is equal to 3 years.

Which of the following statements regarding the sampling distribution of sample means is incorrect?

The standard deviation of the sampling distribution is the standard deviation of the population.

Which of the following statements about the sampling distribution of the sample mean is incorrect? a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n≥30). b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. c) The mean of the sampling distribution of the sample mean is equal to µ. d) The standard deviation of the sampling distribution of the sample mean is equal to σ.

The standard deviation of the sampling distribution of the sample mean is equal to σ.

A numerical measure from a population, such as a population mean, is called

a parameter

A numerical measure from a population, such as a population mean, is called _____.

a parameter

In this problem, the .22 is _____. Refer to Exhibit 7-4 a. a parameter b. a statistic c. the standard error of the mean d. the average content of colognes in the long run

a parameter

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is .22 ounces. In this problem, the value .22 ounces is:

a parameter.

The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is:

a parameter.

The set of all elements of interest in a study is _____.

a population

Cluster sampling is _____.

a probability sampling method

Cluster sampling is:

a probability sampling method.

If we consider the simple random sampling process as an experiment, the sample mean is _____.

a random variable

A numerical measure from a sample, such as a sample mean, is known as

a statistic

A numerical measure from a sample, such as a sample mean, is known as _____.

a statistic

Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for _____.

any sample size

Whenever the population has a normal probability distribution, the sampling distribution of x̄ is a normal probability distribution for _____.

any sample size

A sample of 25 observations is taken from a process. the sampling distribution of p is

approx. normal if np> or equal to 5 and n(1-p)>or equal to 5

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is

approximately normal for large sample sizes

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.

approximately normal for large sample sizes

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is _____.

approximately normal if np ≥ 5 and n(1 - p) ≥ 5

The standard error of the population proportion will become larger

as population proportion approaches 0.50.

In interval estimation, as the sample size becomes larger, the interval estimate:

becomes narrower.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution:

becomes smaller.

When the level of confidence decreases, the margin of error:

becomes smaller.

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion:

becomes wider

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

biased

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the _____.

central limit theorem

The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the

central limit theorem

The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the _____.

central limit theorem

The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size becomes large is based on the:

central limit theorem.

Which of the following sampling methods does NOT lead to probability samples?

convenience sampling

The mean of the population _____. Refer to Exhibit 7-1. a. is 14 b. is 15 c. is 15.1581 d. could be any value

could be any value

As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever a. np ³ 5 b. n(1 - p) ³ 5 c. n ³ 30 d. Both np ³ 5 and n(1 - p) ³ 5 are true.

d. Both np ³ 5 and n(1 - p) ³ 5 are true.

As the sample size increases, the margin of error:

decreases

As the sample size increases, the variability among the sample means _____.

decreases

A simple random sample of size n from an infinite population is a sample selected such that:

each element is selected independently and is selected from the same population.

A simple random sample from a process (an infinite population) is a sample selected such that _____.

each element selected comes from the same population and each element is selected independently

The central limit theorem is important in Statistics because it:

enables reasonably accurate probabilities to be determined for events involving the sample average when the sample size is large regardless of the distribution of the variable.

The Central Limit Theorem is important in statistics because

for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

The expected value of equals the mean of the population from which the sample is drawn _____.

for any sample size

The expected value of x̄ equals the mean of the population from which the sample is drawn _____.

for any sample size

When the population has a normal distribution, the sampling distribution of is normally distributed _____.

for any sample size

When the population has a normal distribution, the sampling distribution of x bar: (x with line over it) is normally distributed _____.

for any sample size

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is:

four times as large as the original sample size. twice as large as the original sample size.

Excel's RAND function _____.

generates random numbers

The central limit theorem states that:

if the sample size n is large, then the sampling distribution of the sample mean can be approximated by a normal distribution.

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

if the shape of the population is symmetrical.

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

increase the sample size to 400.

In general, higher confidence levels provide larger confidence intervals. One way to have high confidence and a small margin of error is to:

increase the sample size.

We can reduce the margin of error in an interval estimate of p by doing any of the following except:

increasing the planning value p* to .5.

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

infinite

For a(n) _____ , it is impossible to construct a sampling frame.

infinite population

It is impossible to construct a frame for a(n) _____.

infinite population

An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known as the:

interval estimate.

The sampling distribution of the sample mean

is the probability distribution showing all possible values of the sample mean

The sampling distribution of the sample mean _____.

is the probability distribution showing all possible values of the sample mean

All of the following are true about the standard error of the mean EXCEPT _____.

it is larger than the standard deviation of the population

Which of the following is an example of a nonprobability sampling technique?

judgment sampling

From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is _____.

less than 2

The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the:

level of significance

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the:

margin of error.

When drawing a sample from a population, the goal is for the sample to:

match the targeted population.

For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval:

must be larger.

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____.

n has the same probability of being selected

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size:

n has the same probability of being selected.

As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when:

n(1 - p) ≥ 5 and np ≥ 5.

In computing the standard error of the mean, the finite population correction factor is NOT used when _____.

n/N ≤ 0.05

In computing the standard error of the mean, the finite population correction factor is used when:

n/N>.05

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is:

nine times as large as the original sample size.

Which of the following best describes the form of the sampling distribution of the sample mean for this situation? a. Approximately normal because the sample size is small relative to the population size b. Approximately normal because of the central limit theorem c. Exactly normal d. None of the answers is correct.

none of the answers are correct

Convenience sampling is an example of _____.

nonprobability sampling technique

Convenience sampling is a:

nonprobability sampling technique.

A sample of 92 observations is taken from an infinite population. The sampling distribution of X(bar) is approximately:

normal because of the central limit theorem.

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately:

normal because of the central limit theorem.

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x bar (x with line over it) is _____.

normal if the population is normally distributed

As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____.

normal probability distribution

As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever _____.

np ≥ 5 and n(1 − p) ≥ 5

The sampling distribution of can be approximated by a normal distribution as long as:

np>=5 and n(1-0p)>=5

Parameters are:

numerical characteristics of a population

A doctor would like to determine if there is a difference between the blood pressure of people who walk every day for 60 minutes and those who walk one day per week for 60 minutes. Fifty of her patients who report that they have routinely walked 60 minutes every day for the past two years and 50 who report that they have walked 60 minutes only one day per week will be identified. The doctor will examine their medical records and collect their blood pressure readings over this two-year period. This is an example of a(n):

observational study.

A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of is approximately normal because _____.

of the central limit theorem

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

only if the population is normally distributed

The standard error of the proportion will become larger as _____.

p approaches .5

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a _____.

point estimate

A single numerical value used as an estimate of a population parameter is known as a_____.

point estimate

A sample statistic, such as x bar (mean: x with line over) , that estimates the value of the corresponding population parameter is known as a _____.

point estimator

A sample statistic, such as x̄, that estimates the value of the corresponding population parameter is known as a _____.

point estimator

Sample statistics, such as x̅ , s, or p̅, that provide the point estimate of the population parameter are known as:

point estimators.

The purpose of statistical inference is to provide information about the _____.

population based upon information contained in the sample

The sampling distribution of is the:

probability distribution of all possible values of the sample proportion.

The sampling distribution of p̅ is the:

probability distribution of all possible values of the sample proportion.

In stratified random sampling:

randomly selected elements within each of the strata form the sample.

In a recent Gallup Poll, the decision was made to increase the size of its random sample of voters from 1500 people to about 4000 people. The purpose of this increase is to:

reduce the standard error of the estimate.

Doubling the size of the sample will _____.

reduce the standard error of the mean to approximately 70% of its current value

Doubling the size of the sample will:

reduce the standard error of the mean.

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

regardless of the shape of the population.

Which of the following is not a symbol for a parameter?

A subset of a population selected to represent the population is a _____.

sample

In point estimation, data from the _____.

sample are used to estimate the population parameter

The margin of error in an interval estimate of the population mean is a function of all of the following except the:

sample mean.

The value of the _____ is used to estimate the value of the population parameter.

sample statistic

The value of the ___________ is used to estimate the value of the population parameter.

sample statistic

A probability distribution for all possible values of a sample statistic is known as a _____.

sampling distribution

The probability distribution of all possible values of the sample proportion is the _____.

sampling distribution of

The probability distribution of all possible values of the sample proportion p bar: (p with line over it) is the _____.

sampling distribution of p bar: (p with line over it)

The probability distribution of all possible values of the sample proportion p̄ is the _____.

sampling distribution of p̄

The probability distribution of all possible values of the sample proportion is the:

sampling distribution of p̅.

The probability distribution of all possible values of the sample proportion p̅, is the:

sampling distribution of p̅.

The probability distribution of all possible values of the sample mean is called the ____.

sampling distribution of the sample mean

The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a:

sampling distribution.

The difference between the value of the sample statistic and the value of the corresponding population parameter is called the _____.

sampling error

The standard deviation of a point estimator is the

standard error

The standard deviation of a point estimator is the _____.

standard error

The standard deviation of all possible mc006-1.jpg values is called the

standard error of the mean

The standard deviation of all possible x bar (mean: x with line over it) values is called the _____.

standard error of the mean

The standard deviation of all possible x values is called the

standard error of the mean

The standard deviation of all possible x̄ values is called the _____.

standard error of the mean

The standard deviation of is referred to as the _____.

standard error of the mean

The standard deviation of x̄ is referred to as the _____.

standard error of the mean

As the sample size increases, the _____.

standard error of the mean decreases

As the sample size increases, the:

standard error of the mean decreases.

The standard deviation of is referred to as the _____.

standard error of the proportion

The standard deviation of p is referred to as the

standard error of the proportion

The standard deviation of a point estimator is called the:

standard error.

Sampling distributions describe the distribution of

statistics

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____.

systematic sampling

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is:

systematic sampling.

In a survey of public opinion concerning state aid to a particular city, every 40th person registered as a voter was interviewed, beginning with a person selected at random from among the first 40 listed. This is an example of:

systematic sampling.

From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the:

t distribution with 29 degrees of freedom.

When "s" is used to estimate "σ," the margin of error is computed by using the:

t distribution.

The population we want to make inferences about is the _____.

target population

The population we want to make inferences about is called the:

target population.

The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

the central limit theorem

The basis for using a normal probability distribution to approximate the sampling distribution of x̄ and p̄ is _____.

the central limit theorem

What is the relationship between the expected value of the sample mean and the population mean?

the expected value of xbar

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is:

the normal distribution.

Stratified random sampling is a method of selecting a sample in which _____.

the population is first divided into groups, and then random samples are drawn from each group

A simple random sample of size n from a finite population of size N is to be selected. Each possible sample should have _____.

the same probability of being selected

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have:

the same probability of being selected.

The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of:

the sample.

When the expected value of the point estimator is equal to the population parameter it estimates it is said to be _____?

unbiased

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

unbiased.

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except:

using .95 as an estimate.

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except:

using σ = 1.

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means _____.

whenever the sample size is more than 5% of the population size

A random sample of 12 four-year-old red pine trees was selected and the diameter (in inches) of each tree's main stem was measured. The resulting observations are as follows: 11.3, 10.7, 12.4, 15.2, 10.1, 12.1 , 16.2, 10.5, 11.4, 11.0, 10.7, and 12.0 Find the point estimate that can be used to estimate the true population mean.

x̅ = 11.97

The expected value of the random variable x bar (mean: x with line over it) is

The sample mean is the point estimator of _____.

The sample mean is the point estimator of:

What is the symbol for the population mean?

To use the normal distribution to approximate the binomial distribution, we need ______ and ______ to be at least 5.

π n and n (1-π )

The sample statistic s is the point estimator of _____.

The sample statistic characteristic s is the point estimator of:

σ.

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