Question 1

The real estate industry claims that it is the best and most effective system to market residential real estate.A survey of randomly selected home sellers in Ontario found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 66% to 76%.Interpret the interval in this context.

Accepted Answer

A) If you sell a home in Ontario,you have an 71% ± 5% chance of using a real estate agent. 
B) We are 99% confident that between 66% and 76% of homes in this survey are sold by a real estate agent. 
C) In 99% of the years,between 66% and 76% of homes in Ontario are sold by a real estate agent. 
D) 99% of all random samples of home sellers in Ontario will show that between 66% and 76% of homes are sold by a real estate agent. 
E) We are 99% confident,based on this sample,that between 66% and 76% of all homes in Ontario are sold by a real estate agent.

Question 2

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.

Question 3

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.

Question 4

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

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.

Question 5

A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home.Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of new home buyers who hired movers.

Accepted Answer

A) 2.08% 
B) 4.96% 
C) 2.48% 
D) 5% 
E) 2.5%

Question 6

In a survey of 280 adults over 50,80% said they were taking vitamin supplements.Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements.

Accepted Answer

A) 10.5% 
B) 13.8% 
C) 6.16% 
D) 4.69% 
E) 17.2%

Question 7

A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective.How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.4%?

Accepted Answer

A) 6,901 
B) 3,452 
C) 8,458 
D) 4,900 
E) Not enough information is given.

Question 8

A mayoral election race is tightly contested.In a random sample of 1,100 likely voters,572 said that they were planning to vote for the current mayor.Based on this sample,would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.

Accepted Answer

The answer of A mayoral election race is tightly contested.In...

Question 9

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 210 people yields a mean cholesterol level of 224 and a standard deviation of 18.Construct a 95% confidence interval for the mean cholesterol level.

Accepted Answer

A) (219.69,228.30) 
B) (219.59,228.40) 
C) (218.53,229.46) 
D) (214.96,233.03) 
E) (221.57,226.43)

Question 10

Of 130 randomly selected adults,32 were found to have high blood pressure.Construct a 95% confidence interval for the percentage of all adults who have high blood pressure.

Accepted Answer

A) (17.2%,32.0%) 
B) (15.8%,33.4%) 
C) (15.0%,34.2%) 
D) (14.9%,34.4%) 
E) (18.4%,30.8%)

Question 11

You want to estimate the average gas price in Canada for a litre of regular unleaded gasoline.You take a random sample of prices from 100 gas stations,recording an average cost of $1.37 and a standard deviation of $0.11.Create a 99% confidence interval for the mean price per litre of regular unleaded gasoline.

Accepted Answer

A) ($1.36,$1.38) 
B) ($1.30,$1.44) 
C) ($1.32,$1.45) 
D) ($1.22,$1.52) 
E) ($1.34,$1.40)

Question 12

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program on a random sample size of 60 and found sick leave at 23%.Create a 95% confidence interval for the proportion of employee sick leave.

Accepted Answer

A) Based on the data,we are 95% confident the proportion of employee sick leave is between 14.9% and 37.1%. 
B) Based on the data,we are 95% confident the proportion of employee sick leave is between 3.76% and 42.24%. 
C) Based on the data,we are 95% confident the proportion of employee sick leave is between 14.9% and 34.1%. 
D) Based on the data,we are 95% confident the proportion of employee sick leave is between 20% and 26%. 
E) Based on the data,we are 95% confident the proportion of employee sick leave is between 12.4% and 33.6%.

Question 13

A company has surveyed a sample of its employees to find out how many might take advantage of a weight loss program.The table below shows the results.Give the 95% confidence interval for Building A for the proportion of employees who would be willing to participate in the program.Based on this interval,can we say that the proportion differs from 11%? At which level of significance are you making this decision? $$\begin{array} { l | c | c | c } 
\text { Group } & \begin{array} { c } 
\text { Number of } \
\text { Employees }
\end{array} & \begin{array} { c } 
\text { Number } \
\text { Surveyed }
\end{array} & \begin{array} { c } 
\text { Percent to } \
\text { Participate }
\end{array} \
\hline \text { Building A } & 5200 & 250 & 8 \% \
\text { Building B } & 1190 & 150 & 6 \% \
\text { Building C } & 248 & 20 & 9 \%
\end{array}$$

Accepted Answer

The answer of A company has surveyed a sample of...

Question 14

Eighty randomly selected students took the calculus final.If the sample mean was 76 and the standard deviation was 8.1,construct a 99% confidence interval for the mean score of all students.

Accepted Answer

A) (71.92,80.08) 
B) (71.94,80.06) 
C) (73.49,78.51) 
D) (73.67,78.33) 
E) (73.49,80.06)

Question 15

The real estate industry claims that it is the best and most effective system to market residential real estate.A survey of randomly selected home sellers in Ontario found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 70% to 80%.Explain what "99% confidence" means in this context.

Accepted Answer

A) There is a 99% chance that the true proportion of home sellers in Ontario who sell their home with a real estate agent is between 70% and 80%. 
B) In 99% of the years,between 70% and 80% of homes in Ontario are sold by a real estate agent. 
C) About 99% of all random samples of home sellers in Ontario will produce a confidence interval that contains the true proportion of homes sold by a real estate agent. 
D) About 99% of all random samples of home sellers in Ontario will find that between 70% and 80% of homes are sold by a real estate agent. 
E) 99% of home sellers in Ontario will sell their home with a real estate agent between 70% and 80% of the time.

Question 16

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.Create a 95% confidence interval for the proportion of housing 1500 sq.ft.

Accepted Answer

A) Based on the data,we are 95% confident the proportion of housing smaller than 1500 sq.ft.is between 57.52% and 74.48%. 
B) Based on the data,we are 95% confident the proportion of housing smaller than 1500 sq.ft.is between 57% and 75%. 
C) Based on the data,we are 95% confident the proportion of housing smaller than 1500 sq.ft.is between 67.25% and 82.75%. 
D) Based on the data,we are 95% confident the proportion of housing smaller than 1500 sq.ft.is between 67.25% and 73.75%. 
E) Based on the data,we are 95% confident the proportion of housing smaller than 1500 sq.ft.is between 47.25% and 84.75%.

Question 17

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)

Question 18

In a survey of 1300 T.V.viewers,30% said they watch network news programs.Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V.viewers who watch network news programs.

Accepted Answer

A) 2.86% 
B) 1.87% 
C) 2.49% 
D) 3.27%

Question 19

A university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation.In previous years,the percentage averaged 13%.He wants the margin of error to be within 4% at a 99% confidence level.What sample size will suffice? Use 2.575 as the critical value for a 99% confidence interval.

Accepted Answer

A) 191 
B) 19 
C) 272 
D) 563 
E) 469

Question 20

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,in 2014 the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Create a 95% confidence interval for the proportion of students (in 2014)who had been retained.

Accepted Answer

A) Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.95% and 7.05%. 
B) Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 4% and 6%. 
C) Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.16% and 8.84%. 
D) Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 2.72% and 7.28%. 
E) Based on the data,we are 95% confident the proportion of students in 2004 who had been retained is between 1.95% and 6.05%.

Exam 16: Confidence Intervals for Proportions

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 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%?

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

A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home.Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of new home buyers who hired movers.

In a survey of 280 adults over 50,80% said they were taking vitamin supplements.Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements.

A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective.How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.4%?

A mayoral election race is tightly contested.In a random sample of 1,100 likely voters,572 said that they were planning to vote for the current mayor.Based on this sample,would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 210 people yields a mean cholesterol level of 224 and a standard deviation of 18.Construct a 95% confidence interval for the mean cholesterol level.

Of 130 randomly selected adults,32 were found to have high blood pressure.Construct a 95% confidence interval for the percentage of all adults who have high blood pressure.

Eighty randomly selected students took the calculus final.If the sample mean was 76 and the standard deviation was 8.1,construct a 99% confidence interval for the mean score of all students.

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.

In a survey of 1300 T.V.viewers,30% said they watch network news programs.Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V.viewers who watch network news programs.

Exam 16: Confidence Intervals for Proportions

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 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%?

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.\$ 42,841 < \mu \text { (Nurse Salary) } < \$ 49,696 .$42,841<μ (Nurse Salary) <$49,696.

A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home.Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of new home buyers who hired movers.

In a survey of 280 adults over 50,80% said they were taking vitamin supplements.Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements.

A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective.How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.4%?

A mayoral election race is tightly contested.In a random sample of 1,100 likely voters,572 said that they were planning to vote for the current mayor.Based on this sample,would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 210 people yields a mean cholesterol level of 224 and a standard deviation of 18.Construct a 95% confidence interval for the mean cholesterol level.

Of 130 randomly selected adults,32 were found to have high blood pressure.Construct a 95% confidence interval for the percentage of all adults who have high blood pressure.

Eighty randomly selected students took the calculus final.If the sample mean was 76 and the standard deviation was 8.1,construct a 99% confidence interval for the mean score of all students.

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.

In a survey of 1300 T.V.viewers,30% said they watch network news programs.Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V.viewers who watch network news programs.

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