Question 1

A 95% confidence interval infers that the population mean is

Accepted Answer

A)  between 0 and 100%. 
B)  within  $\pm$ 1.96 standard deviations of the sample mean. 
C)  within $\pm$ 1.96 standard errors of the sample mean. 
D)  within $\pm$ 1.645 standard deviations of the sample mean. 
E)  too large. 
A)  between 0 and 100%. 
B)  within  $\pm$ 1.96 standard deviations of the sample mean. 
C)  within $\pm$ 1.96 standard errors of the sample mean. 
D)  within $\pm$ 1.645 standard deviations of the sample mean. 
E)  too large.

Question 2

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which one is it?

Accepted Answer

A)  Continuous 
B)  Symmetrical 
C)  Bell-shaped 
D)  t distribution's mean = 0 and standard deviation = 1 
A)  Continuous 
B)  Symmetrical 
C)  Bell-shaped 
D)  t distribution's mean = 0 and standard deviation = 1

Question 3

(i. The point estimate states the range within which a population parameter probably lies. 
(ii). The measure of confidence that one has in the interval estimate is called degree of level of confidence.
(iii) For a sampling distribution of the means, 95% percent of the means would be between $\pm$ 1.96 standard deviations.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) and (ii) are correct statements but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 4

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 99% confidence interval for the mean annual consumption of sugar.

Accepted Answer

A)  23.06 to 30.94 
B)  23.285 to 30.715 
C)  21.97 to 32.03 
D)  23.30 to 30.70 
E)  23.92 to 30.08 
A)  23.06 to 30.94 
B)  23.285 to 30.715 
C)  21.97 to 32.03 
D)  23.30 to 30.70 
E)  23.92 to 30.08

Question 5

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following:   The store manager wonders whether the population mean could have been $50 or $60.

Accepted Answer

A)  Since $60 is within the 95% confidence interval, the population mean is likely to be $60. 
B)  Since $60 is not within the 95% confidence interval, the population mean is not likely to be $60. 
C)  Since $50 is within the 95% confidence interval, the population mean is likely to be $50. 
D)  Since $50 is not within the 95% confidence interval, the population mean is not likely to be $50. 
E)  Since $60 is not within the 95% confidence interval, the population mean is not likely to be $60; however, it is likely to be $50. 
A)  Since $60 is within the 95% confidence interval, the population mean is likely to be $60. 
B)  Since $60 is not within the 95% confidence interval, the population mean is not likely to be $60. 
C)  Since $50 is within the 95% confidence interval, the population mean is likely to be $50. 
D)  Since $50 is not within the 95% confidence interval, the population mean is not likely to be $50. 
E)  Since $60 is not within the 95% confidence interval, the population mean is not likely to be $60; however, it is likely to be $50.

Question 6

How does the t distribution differ from the standard z distribution?

Accepted Answer

A)  Continuous distribution 
B)  Bell-shaped 
C)  Family of distributions 
D)  Symmetrical 
A)  Continuous distribution 
B)  Bell-shaped 
C)  Family of distributions 
D)  Symmetrical

Question 7

A statistics professor wishes to estimate the average mark on a term test for a course that has multiple sections and many students. A survey of some of the students registered for the course reveals the following results:   If 95% and 98% confidence intervals were developed to estimate the true term test mean, what differences would exist?

Accepted Answer

A)  Standard errors 
B)  Interval widths 
C)  t-values 
D)  Both interval widths and t-values 
A)  Standard errors 
B)  Interval widths 
C)  t-values 
D)  Both interval widths and t-values

Question 8

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

Accepted Answer

A)  172 
B)  128 
C)  217 
D)  61 
E)  Over 500 
A)  172 
B)  128 
C)  217 
D)  61 
E)  Over 500

Question 9

A sample of 20 is selected from the population. What is the number of degrees of freedom used to determine the appropriate critical t-value?

Accepted Answer

A)  20 
B)  19 
C)  21 
D)  25 
A)  20 
B)  19 
C)  21 
D)  25

Question 10

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $55,000 with a standard deviation of $2,500. What is the best point estimate of the population mean?

Accepted Answer

A)  $55,000 
B)  $52,500 
C)  400 
D)  $62.5 
A)  $55,000 
B)  $52,500 
C)  400 
D)  $62.5

Question 11

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular candidate. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?

Accepted Answer

A)  78.2% to 81.8% 
B)  69.2% to 86.4% 
C)  76.5% to 83.5% 
D)  77.7% to 82.3% 
A)  78.2% to 81.8% 
B)  69.2% to 86.4% 
C)  76.5% to 83.5% 
D)  77.7% to 82.3%

Question 12

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 40 messages that were not business related. The 95% confidence interval for the population proportion is:

Accepted Answer

A)  0.199 to 0.201 
B)  0.101 to 0.199 
C)  0.07060 to0.12940 
D)  0.0753 to 0.1247 
E)  0.0700 to 0.1000 
A)  0.199 to 0.201 
B)  0.101 to 0.199 
C)  0.07060 to0.12940 
D)  0.0753 to 0.1247 
E)  0.0700 to 0.1000

Question 13

Dr. Patton is a professor of English. Recently she counted the number of misspelled works in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 50 students, the mean number of misspelled words per essay was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of student essays.

Accepted Answer

A)  5.374 to 6.726 
B)  5.161 to 6.939 
C)  5.102 to 6.998 
D)  5.482 to 6.618 
E)  5.445 to 6.3655 
A)  5.374 to 6.726 
B)  5.161 to 6.939 
C)  5.102 to 6.998 
D)  5.482 to 6.618 
E)  5.445 to 6.3655

Question 14

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following:   If 95% and 98% confidence intervals were developed to estimate the true shopping expenditure, what differences would exist?

Accepted Answer

A)  Standard errors 
B)  Interval widths 
C)  t-values 
D)  Both interval widths and t-values 
E)  Both standard errors and interval widths 
A)  Standard errors 
B)  Interval widths 
C)  t-values 
D)  Both interval widths and t-values 
E)  Both standard errors and interval widths

Question 15

College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 90% confidence level and state that the estimation proportion must be within 2 percent of the population proportion. A pilot survey reveals that 10 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

Accepted Answer

A)  910 
B)  1,537 
C)  1,083 
D)  1,221 
E)  2,654 
A)  910 
B)  1,537 
C)  1,083 
D)  1,221 
E)  2,654

Question 16

The mean weight of trucks traveling on a particular section of Highway 401 is not known. A provincial highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?

Accepted Answer

A)  14.7 and 16.9 
B)  13.2 and 17.6 
C)  10.0 and 20.0 
D)  16.1 and 18.1 
A)  14.7 and 16.9 
B)  13.2 and 17.6 
C)  10.0 and 20.0 
D)  16.1 and 18.1

Question 17

Recently, a university surveyed recent graduates of the English Department for their starting salaries. One hundred graduates returned the survey. The average salary was $35,000 with a standard deviation of $2,000. What is the best point estimate of the population mean?

Accepted Answer

A)  $25,000 
B)  $2,000 
C)  $500 
D)  $400 
E)  $35,000 
A)  $25,000 
B)  $2,000 
C)  $500 
D)  $400 
E)  $35,000

Question 18

The following summarizes the amount of snowfall in Ontario over the past number of years.   Determine a 98% confidence interval for the average annual snowfall.

Accepted Answer

A)  [1698, 2046] 
B)  [1665, 2079] 
C)  [1213, 2531] 
D)  [1783, 1961] 
E)  [1659, 2085] 
A)  [1698, 2046] 
B)  [1665, 2079] 
C)  [1213, 2531] 
D)  [1783, 1961] 
E)  [1659, 2085]

Question 19

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 99% confidence interval for the mean annual consumption of sugar.

Accepted Answer

A)  23.06 to 30.94 
B)  22.20 to 31.80 
C)  20.37 to 33.63 
D)  23.30 to 30.70 
E)  23.0 to 30.0 
A)  23.06 to 30.94 
B)  22.20 to 31.80 
C)  20.37 to 33.63 
D)  23.30 to 30.70 
E)  23.0 to 30.0

Question 20

How large a sample of government employees should be taken if we want to estimate with 98% confidence the mean salary to within $2,000? The population standard deviation is assumed to be $10,500. (Round up to the nearest whole number)

Accepted Answer

A)  150 
B)  200 
C)  525 
D)  100 
E)  75 
A)  150 
B)  200 
C)  525 
D)  100 
E)  75

A 95% confidence interval infers that the population mean is

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which one is it?

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 25 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 99% confidence interval for the mean annual consumption of sugar.

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: The store manager wonders whether the population mean could have been $50 or $60.

How does the t distribution differ from the standard z distribution?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

A sample of 20 is selected from the population. What is the number of degrees of freedom used to determine the appropriate critical t-value?

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $55,000 with a standard deviation of $2,500. What is the best point estimate of the population mean?

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular candidate. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 40 messages that were not business related. The 95% confidence interval for the population proportion is:

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: If 95% and 98% confidence intervals were developed to estimate the true shopping expenditure, what differences would exist?

Recently, a university surveyed recent graduates of the English Department for their starting salaries. One hundred graduates returned the survey. The average salary was $35,000 with a standard deviation of $2,000. What is the best point estimate of the population mean?

The following summarizes the amount of snowfall in Ontario over the past number of years. Determine a 98% confidence interval for the average annual snowfall.

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 27 kg with a sample standard deviation of 9 kg. Assume a normal population. Develop a 99% confidence interval for the mean annual consumption of sugar.

How large a sample of government employees should be taken if we want to estimate with 98% confidence the mean salary to within $2,000? The population standard deviation is assumed to be $10,500. (Round up to the nearest whole number)

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 8: Estimation and Confidence Intervals

A 95% confidence interval infers that the population mean is

The t distribution is similar to the z distribution in all BUT ONE of the following characteristics. Which one is it?

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: The store manager wonders whether the population mean could have been $50 or $60.

How does the t distribution differ from the standard z distribution?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

A sample of 20 is selected from the population. What is the number of degrees of freedom used to determine the appropriate critical t-value?

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $55,000 with a standard deviation of $2,500. What is the best point estimate of the population mean?

Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for a particular candidate. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?

College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 40 messages that were not business related. The 95% confidence interval for the population proportion is:

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: If 95% and 98% confidence intervals were developed to estimate the true shopping expenditure, what differences would exist?

Recently, a university surveyed recent graduates of the English Department for their starting salaries. One hundred graduates returned the survey. The average salary was $35,000 with a standard deviation of $2,000. What is the best point estimate of the population mean?

The following summarizes the amount of snowfall in Ontario over the past number of years. Determine a 98% confidence interval for the average annual snowfall.

How large a sample of government employees should be taken if we want to estimate with 98% confidence the mean salary to within $2,000? The population standard deviation is assumed to be $10,500. (Round up to the nearest whole number)

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters