Deck 18: Confidence Intervals for Proportions

Question 1

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.

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

Answer 1

469

Question 2

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

Answer 2

3,452

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?

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

Answer 3

9,466

Question 4

A survey of 300 students at York University revealed that 112 favour an NDP candidate for M.P..Construct a 98% confidence interval for the percentage of all York University students who favour an NDP candidate.

A)(26.7%,47.9%)
B)(17.8%,56.8%)
C)(30.1%,44.5%)
D)(30.8%,43.8%)
E)(31.9%,42.8%)

Question 5

In a survey of 1,300 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.

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

Question 6

Of 346 items tested,12 are found to be defective.Construct a 98% confidence interval for the percentage of all such items that are defective.

A)(1.18%,5.76%)
B)(0.93%,6.00%)
C)(3.34%,3.59%)
D)(1.85%,5.09%)
E)(0.13%,6.80%)

Question 7

A survey of 865 people in one city reveals that 408 have visited a Tim Hortons location in the past week.Construct a 95% confidence interval for the percentage of all people in this city who have visited a Tim Hortons location in the last week.

A)(43.8%,50.5%)
B)(44.4%,50.0%)
C)(46.9%,47.5%)
D)(42.3%,52.0%)
E)(43.1%,51.2%)

Question 8

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

Question 9

Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.

A)(7.90%,16.9%)
B)(8.61%,16.2%)
C)(9.22%,15.6%)
D)(7.90%,17.4%)
E)(7.41%,17.4%)

Question 10

A study involves 673 randomly selected deaths,with 34 of them caused by accidents.Construct a 98% confidence interval for the percentage of all deaths that are caused by accidents.

A)(3.40%,6.71%)
B)(3.66%,6.45%)
C)(3.8%,6.4%)
D)(2.87%,7.23%)
E)(3.09%,7.02%)

Question 11

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.

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

Question 12

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

Question 13

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.

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

Question 14

A pollster wishes to estimate the true proportion of voters in Ottawa,Ontario who support the Conservative party.How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to within 4%?

A)846
B)1037
C)423
D)601
E)Not enough information is given.

Question 15

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.

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 16

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.

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 17

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

Question 18

Of 88 adults selected randomly from one town,60 have health insurance.Construct a 90% confidence interval for the percentage of all adults in the town who have health insurance.

A)(58.5%,77.9%)
B)(61.0%,75.4%)
C)(56.6%,79.8%)
D)(55.4%,81.0%)
E)(60.0%,76.3%)

Question 19

When 278 college students are randomly selected and surveyed,it is found that 110 own a car.Construct a 99% confidence interval for the percentage of all college students who own a car.

A)(34.7%,44.4%)
B)(18.6%,60.6%)
C)(33.8%,45.3%)
D)(32.0%,47.1%)
E)(32.7%,46.4%)

Question 20

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)(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 21

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 90% confidence interval for the proportion of homes that are sold by a real estate agent is 75% ± 6%.Explain why each of these conclusions is not correct.
a)Between 69% and 81% of all homes in Ontario are sold by a real estate agent.
b)90% of all random samples of home sellers in Ontario will show that 75% of homes are sold by a real estate agent.
c)90% of all random samples of home sellers in Ontario will show that 69% to 81% of homes are sold by a real estate agent.
d)We are 90% sure that between 69% and 81% of homes in this sample were sold by a real estate agent.

Question 22

A poll of 2841 registered voters in a certain town indicated that 70% would vote for the Liberal Party of Canada.The margin of error for this poll was 2%.

A)98%
B)90%
C)95%
D)99%
E)Not enough information is given.

Question 23

A newspaper reports that 62% of city residents have visited one of the city parks in the last year.The article adds that the poll is based on a random sample of 996 residents and has a margin of error of 2.5%.

A)95%
B)90%
C)99%
D)98%
E)Not enough information is given.

Question 24

After conducting a survey,a researcher wishes to cut the standard error (and thus the margin of error)to
Of its original value.How will the necessary sample size change?

A)It will increase by a factor of 3.
B)It will decrease by a factor of 3.
C)It will increase by a factor of 9.
D)It will decrease by a factor of 9.
E)Not enough information is given.

Question 25

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.

Question 26

A mayoral election race is tightly contested.In a random sample of 1,900 likely voters,1,007 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.

Question 27

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?

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 28

In a poll of 553 voters in a certain city,64% said that they supported the NDP in an upcoming election.The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence).Make a statement about the adequacy of the sample size for the given margin of error.

A)The sample size is too large to achieve the stated margin of error.
B)For the given sample size,the margin of error should be smaller than stated
C)The sample size is too small to achieve the stated margin of error.
D)The reported margin of error is consistent with the sample size.
E)There is not enough information to determine whether the margin of error is consistent with the sample size.

Question 29

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?

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

Question 30

In a poll of 2,778 voters in a certain city,77% said that they supported the Conservative Party of Canada.The margin of error in the poll was reported as 6 percentage points (with a 95% degree of confidence).Make a statement about the adequacy of the sample size for the given margin of error.

A)The stated margin of error could be achieved with a larger sample size.
B)The sample size is too small to achieve the stated margin of error.
C)The reported margin of error is consistent with the sample size.
D)The stated margin of error could be achieved with a smaller sample size.
E)There is not enough information to determine whether the margin of error is consistent with the sample size.

Question 31

A poll of 565 home sellers found that 25.1% were trying to sell their home without a real estate agent.The margin of error for this poll was 3%.

A)99%
B)90%
C)98%
D)95%
E)Not enough information is given.

Question 32

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.

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 33

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)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 34

A newspaper reports that the Prime Minister's approval rating stands at 60%.The article adds that the poll is based on a random sample of 1,040 adults and has a margin of error of 2.5%.

A)99%
B)98%
C)90%
D)95%
E)Not enough information is given.

Question 35

A newspaper reports that 58% of farmers are planning to plant genetically modified crops this year.The article adds that the poll is based on a random sample of 798 farmers and has a margin of error of 4.5%.

A)99%
B)98%
C)95%
D)90%
E)Not enough information is given.

Question 36

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.

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)

Question 37

A political party is interested in finding out what kind of popular support they might expect on an environmental initiative.Similar issues have gotten 87% support.The committee will set up a polling program to assure 95% confidence that the margin of error is less than 9%.What sample size will suffice?

A)162
B)5
C)54
D)48
E)38

Question 38

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)(71.92,80.08)
B)(71.94,80.06)
C)(73.49,78.51)
D)(75.63,82.37)
E)(73.49,80.06)

Question 39

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.

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 40

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.

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 41

A local bank needs information concerning the checking account balances of its local customers.A random sample of 144 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29.Find a 98% confidence interval for the true mean checking account balance for local customers.

A)($592.52,$735.76)
B)($605.85,$722.43)
C)($555.65,$735.76)
D)($493.71,$834.57)
E)($453.56,$874.72)

Question 42

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.

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

Question 43

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 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

A)95% of reduced fat cookies have between 3.4 and 5 grams of fat.
B)We are 95% sure that the average amount of fat in the cookies in this study was between 3.4 and 5 grams.
C)We are 95% confident that the mean fat in all cookies is between 3.4 and 5 grams.
D)95% of the cookies in the sample had between 3.4 and 5 grams of fat.
E)You are 95% confident that the mean fat in reduced fat cookies is between 3.4 and 5 grams of fat.

Question 44

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.From your sample of 15 gas stations,you calculate a 95% confidence interval of ($1.34,$1.40)

A)You are 95% sure that the average price for a litre of regular unleaded gasoline in your city is between $1.34 and $1.40.
B)You are 95% confident that the average price for a litre of regular unleaded gasoline in the country is within $0.03 of $1.37.
C)You are 95% sure that gas stations in this sample have average costs between $1.34 and $1.40.
D)95% of all samples of gas stations will have average costs between $1.34 and $1.40.
E)If you took many samples of gas stations in your city,about 95% of them would produce this confidence interval.

Question 45

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

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 46

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.

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 47

Among a sample of 100 students selected at random from one college,the mean number of siblings is 1.4 with a standard deviation of 1.3.Find a 95% confidence interval for the mean number of siblings for all students at this college.

A)(1.08,1.73)
B)(1.36,1.44)
C)(61.8,66.2)
D)(0.95,1.45)
E)(1.24,1.44)

Question 48

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)(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 49

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)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 50

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.

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 51

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)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 52

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.

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 53

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.

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 54

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)(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 55

How tall is the average student on your campus? To determine this,you measure the height,in centimetres,of a random sample of 200 students and calculate the following confidence interval with 95% confidence:
155.72 < μ(height)< 181.20

A)There's a 95% chance of a classmate being between 155.72 and 181.20 cm tall.
B)We're 95% sure that the average height of your statistics classmates is between 155.72 and 181.20 cm.
C)The average height of your classmates is between 155.72 and 181.20 cm.
D)We can be 95% sure that statistics students are between 155.72 and 181.20 cm tall.
E)95 of your 100 classmates are between 155.72 and 181.20 cm tall.

Question 56

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%.

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.