Question 1

Of 125 adults selected randomly from one town,28 of them smoke.Construct a 99% confidence interval for the percentage of all adults in the town who smoke.

Accepted Answer

A) (15.1%,29.7%) 
B) (13.7%,29.7%) 
C) (12.8%,30.3%) 
D) (16.2%,28.6%) 
E) (13.7%,31.1%) 
A) (15.1%,29.7%) 
B) (13.7%,29.7%) 
C) (12.8%,30.3%) 
D) (16.2%,28.6%) 
E) (13.7%,31.1%)

Question 2

Of 314 randomly selected medical students,25 said that they planned to work in a rural community.Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community.

Accepted Answer

A) (4.40%,11.5%) 
B) (4.97%,11.0%) 
C) (5.45%,10.5%) 
D) (4.03%,11.9%) 
E) (7.02%,8.90%) 
A) (4.40%,11.5%) 
B) (4.97%,11.0%) 
C) (5.45%,10.5%) 
D) (4.03%,11.9%) 
E) (7.02%,8.90%)

Question 3

A survey of shoppers is planned to see what percentage use credit cards.Prior surveys suggest 56% of shoppers use credit cards.How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence?

Accepted Answer

A) 6,664 
B) 8,519 
C) 9,466 
D) 16,338 
E) 21,513 
A) 6,664 
B) 8,519 
C) 9,466 
D) 16,338 
E) 21,513

Question 4

A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school.Find the margin of error for this poll if we want 90% confidence in our estimate of the percent of residents in favor of this proposed referendum.

Accepted Answer

A) 3.53% 
B) 2.43% 
C) 10% 
D) 5% 
E) 7.06% 
A) 3.53% 
B) 2.43% 
C) 10% 
D) 5% 
E) 7.06%

Question 5

A survey found that 79% of a random sample of 1024 Canadian adults approved of cloning endangered animals.Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of Canadian adults who approve of cloning endangered animals.

Accepted Answer

A) 4.56% 
B) 21.4% 
C) 5.43% 
D) 2.49% 
E) 2.09% 
A) 4.56% 
B) 21.4% 
C) 5.43% 
D) 2.49% 
E) 2.09%

Question 6

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 99% confidence level,the margin of error for this estimate is 3.99%.If we only want to be 90% confident,how will the margin of error change?

Accepted Answer

A) Since less confidence allows a narrower interval,the margin of error will be larger. 
B) Since less confidence allows a narrower interval,the margin of error will be smaller. 
C) Since less confidence allows a wider interval,the margin of error will be larger. 
D) Since less confidence allows a wider interval,the margin of error will be smaller. 
E) There is not enough information to determine the effect on the margin of error. 
A) Since less confidence allows a narrower interval,the margin of error will be larger. 
B) Since less confidence allows a narrower interval,the margin of error will be smaller. 
C) Since less confidence allows a wider interval,the margin of error will be larger. 
D) Since less confidence allows a wider interval,the margin of error will be smaller. 
E) There is not enough information to determine the effect on the margin of error.

Question 7

Analysis of a random sample of 250 Nova Scotia nurses produced a 95% confidence interval for the mean annual salary of $42,841 < μ(Nurse Salary)< $49,696.

Accepted Answer

A) We are 95% confident that the interval from $42,841 to $49,696 contains the true mean salary of all Nova Scotia nurses. 
B) We are 95% confident that the average nurse salary in the Canada is between $42,841 and $49,696. 
C) About 95% of the nurses surveyed earn between $42,841 and $49,696. 
D) About 95% of Nova Scotia nurses earn between $42,841 and $49,696. 
E) If we took many random samples of Nova Scotia nurses,about 95% of them would produce this confidence interval. 
A) We are 95% confident that the interval from $42,841 to $49,696 contains the true mean salary of all Nova Scotia nurses. 
B) We are 95% confident that the average nurse salary in the Canada is between $42,841 and $49,696. 
C) About 95% of the nurses surveyed earn between $42,841 and $49,696. 
D) About 95% of Nova Scotia nurses earn between $42,841 and $49,696. 
E) If we took many random samples of Nova Scotia nurses,about 95% of them would produce this confidence interval.

Question 8

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 90% confidence level,the margin of error for this estimate is 2.5%.If we want to be 99% confident,how will the margin of error change?

Accepted Answer

A) Since more confidence requires a more narrow interval,the margin of error will be larger. 
B) Since more confidence requires a more narrow interval,the margin of error will be smaller. 
C) Since more confidence requires a wider interval,the margin of error will be larger. 
D) Since more confidence requires a wider interval,the margin of error will be smaller. 
E) There is not enough information to determine the effect on the margin of error. 
A) Since more confidence requires a more narrow interval,the margin of error will be larger. 
B) Since more confidence requires a more narrow interval,the margin of error will be smaller. 
C) Since more confidence requires a wider interval,the margin of error will be larger. 
D) Since more confidence requires a wider interval,the margin of error will be smaller. 
E) There is not enough information to determine the effect on the margin of error.

Question 9

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 221 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

Accepted Answer

A) We are 90% confident that 90% of people in the city have a cholesterol level between 207 and 231. 
B) The researcher can be 90% confident that the mean cholesterol level for people in his city is between 207 and 231. 
C) 90% of the people sampled have cholesterol levels between 207 and 231. 
D) If we took many random samples of people in the city,about 9 out of 10 of them could produce a confidence interval of (207,231). 
E) About 9 out of 10 people in the researcher's city have cholesterol levels between 207 and 231. 
A) We are 90% confident that 90% of people in the city have a cholesterol level between 207 and 231. 
B) The researcher can be 90% confident that the mean cholesterol level for people in his city is between 207 and 231. 
C) 90% of the people sampled have cholesterol levels between 207 and 231. 
D) If we took many random samples of people in the city,about 9 out of 10 of them could produce a confidence interval of (207,231). 
E) About 9 out of 10 people in the researcher's city have cholesterol levels between 207 and 231.

Question 10

An advertising firm wants to confirm estimates that 18% of households will buy something on the internet next year.What sample size will produce a margin of error of 7% with 90% confidence level?

Accepted Answer

A) 116 
B) 82 
C) 73 
D) 246 
E) 6 
A) 116 
B) 82 
C) 73 
D) 246 
E) 6

Question 11

A random sample of clients at a weight loss centre were given a dietary supplement to see if it would promote weight loss.The centre reported that the 100 clients lost an average of 47 pounds,and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±9 pounds.

Accepted Answer

A) 95% of the people who use this supplement will lose between 38 and 56 pounds. 
B) The average weight loss of clients who take this supplement will be between 38 and 56 pounds. 
C) 95% of the clients in the study lost between 38 and 56 pounds. 
D) We are 95% sure that the average weight loss among the clients in this study was between 38 and 56 pounds. 
E) We are 95% confident that the mean weight loss produced by the supplement in weight loss centre clients is between 38 and 56 pounds. 
A) 95% of the people who use this supplement will lose between 38 and 56 pounds. 
B) The average weight loss of clients who take this supplement will be between 38 and 56 pounds. 
C) 95% of the clients in the study lost between 38 and 56 pounds. 
D) We are 95% sure that the average weight loss among the clients in this study was between 38 and 56 pounds. 
E) We are 95% confident that the mean weight loss produced by the supplement in weight loss centre clients is between 38 and 56 pounds.

Question 12

How many unpopped kernels are left when you pop a bag of microwave popcorn? Quality control personnel at Yummy Popcorn take a random sample of 80 bags of popcorn.They pop each bag in a microwave and then count the number of unpopped kernels.The following interval is produced:
T-interval for μ : with 99% Confidence,
11 < μ(unpopped)< 25

Accepted Answer

A) The average number of unpopped kernels in a bag of Yummy popcorn is between 11 and 25 kernels. 
B) We are 99% sure that the average number of unpopped kernels in bags of Yummy brand popcorn is between 11 and 25 kernels. 
C) We are 99% confident that the average number of unpopped kernels in microwave popcorn bags is between 11 and 25. 
D) 99% of all samples of Yummy popcorn will produce this confidence interval. 
E) About 99% of the sampled bags had between 11 and 25 unpopped kernels. 
A) The average number of unpopped kernels in a bag of Yummy popcorn is between 11 and 25 kernels. 
B) We are 99% sure that the average number of unpopped kernels in bags of Yummy brand popcorn is between 11 and 25 kernels. 
C) We are 99% confident that the average number of unpopped kernels in microwave popcorn bags is between 11 and 25. 
D) 99% of all samples of Yummy popcorn will produce this confidence interval. 
E) About 99% of the sampled bags had between 11 and 25 unpopped kernels.

Question 13

Data collected by child development scientists produced the following 90% confidence interval for the average age (in months)at which children say their first word: 10.2 < μ(age)< 13.5.

Accepted Answer

A) 90% of the children in this sample said their first word when they were between 10.2 and 13.5 months old. 
B) We are 90% sure that the average age at which children in this sample said their first word was between 10.2 and 13.5 months. 
C) Based on this sample,we can say,with 90% confidence,that the mean age at which children say their first word is between 10.2 and 13.5 months. 
D) We are 90% sure that a child will say his first word when he is between 10.2 and 13.5 months old. 
E) If we took many random samples of children,about 90% of them would produce this confidence interval. 
A) 90% of the children in this sample said their first word when they were between 10.2 and 13.5 months old. 
B) We are 90% sure that the average age at which children in this sample said their first word was between 10.2 and 13.5 months. 
C) Based on this sample,we can say,with 90% confidence,that the mean age at which children say their first word is between 10.2 and 13.5 months. 
D) We are 90% sure that a child will say his first word when he is between 10.2 and 13.5 months old. 
E) If we took many random samples of children,about 90% of them would produce this confidence interval.

Question 14

A credit union took a random sample of 400 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2,185 < μ(balance)< $3,846.

Accepted Answer

A) We are 90% confident that the mean checking account balance at this credit union is between $2,185 and $3,846,based on this sample. 
B) We are 90% sure that the mean balance for checking accounts in the sample was between $2,185 and $3,846. 
C) If we took random samples of checking accounts at this credit union,about nine out of ten of them would produce this confidence interval. 
D) About 9 out of 10 people have a checking account balance between $2,185 and $3,846. 
E) We are 90% confident that the mean checking account balance in the U.S.is between $2,185 and $3,846. 
A) We are 90% confident that the mean checking account balance at this credit union is between $2,185 and $3,846,based on this sample. 
B) We are 90% sure that the mean balance for checking accounts in the sample was between $2,185 and $3,846. 
C) If we took random samples of checking accounts at this credit union,about nine out of ten of them would produce this confidence interval. 
D) About 9 out of 10 people have a checking account balance between $2,185 and $3,846. 
E) We are 90% confident that the mean checking account balance in the U.S.is between $2,185 and $3,846.

Question 15

A sociologist develops a test to measure attitudes about public transportation,and 100 randomly selected subjects are given the test.Their mean score is 76.2 and their standard deviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects.

Accepted Answer

A) (64.2,88.2) 
B) (72.0,80.4) 
C) (67.7,84.7) 
D) (64.2,83.2) 
E) (74.6,77.8) 
A) (64.2,88.2) 
B) (72.0,80.4) 
C) (67.7,84.7) 
D) (64.2,83.2) 
E) (74.6,77.8)

Question 16

How much fat do reduced fat cookies typically have? You take a random sample of 120 reduced-fat cookies and test them in a lab,finding a mean fat content of 3.2 grams and a standard deviation of 1.9 grams of fat.Create a 99% confidence interval for the mean grams of fat.

Accepted Answer

A) (2.10,4.30) 
B) (2.75,3.66) 
C) (2.79,3.61) 
D) (2.78,3.62) 
E) (2.80,3.60) 
A) (2.10,4.30) 
B) (2.75,3.66) 
C) (2.79,3.61) 
D) (2.78,3.62) 
E) (2.80,3.60)

Question 17

A random sample of 64 statistics students at a small college were given a surprise quiz out of 40 marks.The average score was 27 with a standard deviation of 5.Find a 95% confidence interval for the mean quiz score for all statistics students at this college.

Accepted Answer

A) (26.4,27.6) 
B) (62.1,65.9) 
C) (26.8,27.2) 
D) (25.8,28.3) 
E) (26.4,27.2) 
A) (26.4,27.6) 
B) (62.1,65.9) 
C) (26.8,27.2) 
D) (25.8,28.3) 
E) (26.4,27.2)

Question 18

How tall is the average student on your campus? To determine this,you measure the height of a random sample of 200 students,finding a mean height of 166.60 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your fellow students.

Accepted Answer

A) (165.94,167.26) 
B) (167.02,168.97) 
C) (165.82,167.38) 
D) (167.73,168.27) 
E) (166.99,169.01) 
A) (165.94,167.26) 
B) (167.02,168.97) 
C) (165.82,167.38) 
D) (167.73,168.27) 
E) (166.99,169.01)

Question 19

A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake.How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 6%?

Accepted Answer

A) 188 
B) 461 
C) 376 
D) 267 
E) Not enough information is given. 
A) 188 
B) 461 
C) 376 
D) 267 
E) Not enough information is given.

Question 20

A laboratory tested 60 chicken eggs and found that the mean amount of cholesterol was 241 milligrams with s = 14.7 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Accepted Answer

A) (230.2,237.8) 
B) (231.5,248.6) 
C) (231.7,250.3) 
D) (233.4,248.6) 
E) (231.7,250.5) 
A) (230.2,237.8) 
B) (231.5,248.6) 
C) (231.7,250.3) 
D) (233.4,248.6) 
E) (231.7,250.5)

Exam 18: Confidence Intervals for Proportions

Of 125 adults selected randomly from one town,28 of them smoke.Construct a 99% confidence interval for the percentage of all adults in the town who smoke.

Of 314 randomly selected medical students,25 said that they planned to work in a rural community.Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community.

A survey of shoppers is planned to see what percentage use credit cards.Prior surveys suggest 56% of shoppers use credit cards.How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence?

A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school.Find the margin of error for this poll if we want 90% confidence in our estimate of the percent of residents in favor of this proposed referendum.

A survey found that 79% of a random sample of 1024 Canadian adults approved of cloning endangered animals.Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of Canadian adults who approve of cloning endangered animals.

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 99% confidence level,the margin of error for this estimate is 3.99%.If we only want to be 90% confident,how will the margin of error change?

Analysis of a random sample of 250 Nova Scotia nurses produced a 95% confidence interval for the mean annual salary of $42,841 < μ(Nurse Salary)< $49,696.

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 90% confidence level,the margin of error for this estimate is 2.5%.If we want to be 99% confident,how will the margin of error change?

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 221 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

An advertising firm wants to confirm estimates that 18% of households will buy something on the internet next year.What sample size will produce a margin of error of 7% with 90% confidence level?

Data collected by child development scientists produced the following 90% confidence interval for the average age (in months)at which children say their first word: 10.2 < μ(age)< 13.5.

A credit union took a random sample of 400 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2,185 < μ(balance)< $3,846.

A sociologist develops a test to measure attitudes about public transportation,and 100 randomly selected subjects are given the test.Their mean score is 76.2 and their standard deviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects.

How much fat do reduced fat cookies typically have? You take a random sample of 120 reduced-fat cookies and test them in a lab,finding a mean fat content of 3.2 grams and a standard deviation of 1.9 grams of fat.Create a 99% confidence interval for the mean grams of fat.

A random sample of 64 statistics students at a small college were given a surprise quiz out of 40 marks.The average score was 27 with a standard deviation of 5.Find a 95% confidence interval for the mean quiz score for all statistics students at this college.

How tall is the average student on your campus? To determine this,you measure the height of a random sample of 200 students,finding a mean height of 166.60 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your fellow students.

A researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake.How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 6%?

A laboratory tested 60 chicken eggs and found that the mean amount of cholesterol was 241 milligrams with s = 14.7 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

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