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 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.

Accepted Answer

The answer of The real estate industry claims that it...

Question 2

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%.

Accepted Answer

The answer of A poll of 2841 registered voters in...

Question 3

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%.

Accepted Answer

The answer of A newspaper reports that 62% of city...

Question 4

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?

Accepted Answer

The standard error is proportional to the inverse square root of the sample size. To cut the standard error by a factor of 3, we need to increase the sample size by a factor of 9 (i.e., 3 squared).

Question 5

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

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Question 6

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.

Accepted Answer

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

Question 7

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

Lower confidence levels result in narrower confidence intervals, thus reducing the margin of error.

Question 8

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.

Accepted Answer

A sample size of 553 is considered a large enough sample size for a population of voters in a certain city. The reported margin of error of 4 percentage points with a 95% degree of confidence is consistent with the sample size. Therefore, the sample size is adequate for the given margin of error.

Question 9

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

The answer of An advertising firm wants to confirm estimates...

Question 10

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.

Accepted Answer

The answer of In a poll of 2,778 voters in...

Question 11

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%.

Accepted Answer

The answer of A poll of 565 home sellers found...

Question 12

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

The statement "99% confidence interval" means that if we were to repeatedly take random samples from the population of home sellers in Ontario and construct 99% confidence intervals for the proportion of homes sold by a real estate agent, about 99% of those intervals would contain the true proportion of homes sold by a real estate agent. In other words, we can be 99% confident that the true proportion is between 70% and 80% based on this particular sample.

Question 13

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

When we want to be more confident, we need to increase the width of the interval or increase the margin of error. Therefore, the margin of error will be larger for a 99% confidence level compared to a 90% confidence level, making choice C the correct answer.

Question 14

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%.

Accepted Answer

The answer of A newspaper reports that the Prime Minister's...

Question 15

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%.

Accepted Answer

The answer of A newspaper reports that 58% of farmers...

Question 16

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

The answer of A laboratory tested 60 chicken eggs and...

Question 17

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?

Accepted Answer

We need to use the formula for sample size calculation for proportions:

n = (z^2 * p * q) / E^2

where:
z = z-score for the level of confidence (95% = 1.96)
p = estimated proportion (87% = 0.87)
q = 1 - p
E = maximum margin of error (9% = 0.09)

Plugging in the values:

n = (1.96^2 * 0.87 * 0.13) / 0.09^2
n = 53.64
n ≈ 54 (rounded up)

Therefore, the best choice is C with a sample size of 54.

Question 18

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

The answer of Eighty randomly selected students took the calculus...

Question 19

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

This is the best choice because it accurately reflects the interpretation of the confidence interval in the context of the survey. The interval represents our level of confidence that the true proportion of homes sold by a real estate agent in Ontario falls within the range of 66% to 76%, based on the sample collected. The use of "all homes in Ontario" instead of "homes in this survey" is important because it expands the scope of the inference to the population of interest. The expression "we are 99% confident" also aligns with the level of confidence stated in the problem.

Question 20

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

The answer of A sociologist develops a test to measure...

Quiz 18: Confidence Intervals for Proportions