Question 1

The large sample confidence interval formula for estimating p can always safely be used if  .

Accepted Answer

False

Question 2

If the distribution of a population is symmetric, both the mean and median give unbiased estimates of the population mean. What criteria would you consider in choosing which statistic to use if you wanted to estimate the population mean?

Accepted Answer

Choose the statistic that has the lower variability (smaller standard deviation). If the distribution is normal, this will be the sample mean. If the distribution has heavy tails, then the sample median may be a better choice.

Question 3

The standard error of  is  .

Accepted Answer

False

Question 4

Using an unbiased statistic guarantees that there will be no systematic tendency to under- or overestimate the value of the population characteristic and that estimates will almost always be relatively close to the true value.

Accepted Answer

An unbiased statistic means that the expected value of the statistic equals the true population parameter, but it does not guarantee that individual estimates will be close to the true value; variability of the statistic can still result in individual estimates being far from the true value.

Question 5

What is the difference between an unbiased statistic and a biased statistic?

Accepted Answer

The answer of What is the difference between an unbiased...

Question 6

A 90% confidence interval for a population proportion calculated using data from a random sample of size n = 51 is (0.573, 0.787). Which of the following is the 95% confidence interval calculated from the same data? ​

Accepted Answer

The 95% confidence interval will be wider than the 90% confidence interval due to the higher confidence level requiring a larger margin of error. Among the options, only choice C (0.553, 0.807) is wider than the given 90% interval (0.573, 0.787).

Question 7

What proportion of college students have used cell phones to cheat on an exam? ​
Suppose you have been asked to estimate this proportion for students enrolled at a large college. Make an estimate of the margin of error (M) when there are 151 students in the survey. Assume a 95% confidence level.
​

Accepted Answer

The answer of What proportion of college students have used...

Question 8

Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:    Which statistic would you recommend?

Accepted Answer

The answer of Three different statistics are being considered for...

Question 9

Chuck has decided to increase the size of the sample he uses to estimate a population proportion. ​
What is the effect on the width of the associated confidence interval?
​

Accepted Answer

Increasing the sample size generally leads to a decrease in the width of the confidence interval, making the estimate more precise. This is because the standard error, which is inversely related to the square root of the sample size, decreases as the sample size increases.

Question 10

An unbiased statistic is one that ​

Accepted Answer

An unbiased statistic is defined as a statistic that, on average, does not overestimate or underestimate the parameter it is estimating. This means that the expected value of the statistic is equal to the parameter it is intended to estimate, making choice E the correct definition of an unbiased statistic.

Question 11

A random sample will be selected from the population of all adult residents of a particular city. The sample proportion  will be used to estimate p, the proportion of all adult residents who are registered to vote. For which of the following situations will the estimate tend to be closest to the actual value of p? ​
I. 
 II. 
 III.  ​

Accepted Answer

The answer of A random sample will be selected from...

Question 12

The sampling distribution of p tends to be more spread out for larger sample sizes than for smaller sample sizes.

Accepted Answer

The sampling distribution of p (proportion) tends to be less spread out for larger sample sizes due to the decrease in the standard error as the sample size increases.

Question 13

Jasmine has decided to decrease the confidence level in her estimation of a population proportion. What is the effect on the width of the associated confidence interval? ​
​

Accepted Answer

Decreasing the confidence level results in a narrower (smaller) confidence interval because a lower confidence level means you are accepting a higher chance of error, thus requiring less range to capture the true population parameter.

Question 14

A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and can't be used. A large shipment of plastic handles is received. How many handles from the shipment should be inspected in order to estimate p, the proportion of defective handles in the shipment, with a margin of error of 0.13 or less? (Assume a confidence level of 95%). ​

Accepted Answer

To estimate the proportion with a margin of error of 0.13 at a 95% confidence level, the sample size can be calculated using the formula for sample size in proportion estimation: n = (Z^2 * p * (1-p)) / E^2. Assuming p = 0.5 for maximum variability, Z = 1.96 for 95% confidence, and E = 0.13, the calculation gives approximately 57 handles.

Question 15

Holding all other elements equal, an increase in sample size will result in a wider confidence interval.

Accepted Answer

The answer of Holding all other elements equal, an increase...

Question 16

A statistic that is unbiased with a small standard error is likely to result in an estimate that is close to the actual value of the population characteristic.

Accepted Answer

An unbiased statistic means the expected value of the estimate is equal to the population parameter it estimates, and a small standard error indicates the estimates are consistently close to the true value, making the estimate likely close to the actual population characteristic.

Question 17

When choosing a statistic for computing an estimate, what factors should be considered?

Accepted Answer

The answer of When choosing a statistic for computing an...

Question 18

To estimate the proportion of faculty at a state university who own a home, a random sample of faculty is selected. For which of the following combinations of n and  would it be appropriate to use the confidence interval  to estimate the population proportion? ​

Accepted Answer

The answer of To estimate the proportion of faculty at...

Question 19

Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95% confidence interval for the proportion that has Internet access is (0.73, 0.79). Which of the following is a correct interpretation of the 95% confidence level? ​

Accepted Answer

The correct interpretation of a 95% confidence level is that if we were to take many samples and construct a confidence interval for each, about 95% of these intervals would contain the true population proportion.

Question 20

All else being equal, the higher the confidence level, the wider the confidence interval.

Accepted Answer

This is because a higher confidence level means that we want to be more confident that the true population parameter falls within the interval, so we need to widen the interval to accommodate a greater range of possible values.

Quiz 9: Estimating a Population Proportion

The large sample confidence interval formula for estimating p can always safely be used if .

If the distribution of a population is symmetric, both the mean and median give unbiased estimates of the population mean. What criteria would you consider in choosing which statistic to use if you wanted to estimate the population mean?

The standard error of is .

Using an unbiased statistic guarantees that there will be no systematic tendency to under- or overestimate the value of the population characteristic and that estimates will almost always be relatively close to the true value.

What is the difference between an unbiased statistic and a biased statistic?

A 90% confidence interval for a population proportion calculated using data from a random sample of size n = 51 is (0.573, 0.787) . Which of the following is the 95% confidence interval calculated from the same data?

What proportion of college students have used cell phones to cheat on an exam? Suppose you have been asked to estimate this proportion for students enrolled at a large college. Make an estimate of the margin of error (M) when there are 151 students in the survey. Assume a 95% confidence level.

Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which statistic would you recommend?

Chuck has decided to increase the size of the sample he uses to estimate a population proportion. What is the effect on the width of the associated confidence interval?

An unbiased statistic is one that

The sampling distribution of p tends to be more spread out for larger sample sizes than for smaller sample sizes.

Jasmine has decided to decrease the confidence level in her estimation of a population proportion. What is the effect on the width of the associated confidence interval?

Holding all other elements equal, an increase in sample size will result in a wider confidence interval.

A statistic that is unbiased with a small standard error is likely to result in an estimate that is close to the actual value of the population characteristic.

When choosing a statistic for computing an estimate, what factors should be considered?

To estimate the proportion of faculty at a state university who own a home, a random sample of faculty is selected. For which of the following combinations of n and would it be appropriate to use the confidence interval to estimate the population proportion?

Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95% confidence interval for the proportion that has Internet access is (0.73, 0.79) . Which of the following is a correct interpretation of the 95% confidence level?

All else being equal, the higher the confidence level, the wider the confidence interval.

Quiz 9: Estimating a Population Proportion

The large sample confidence interval formula for estimating p can always safely be used if .

If the distribution of a population is symmetric, both the mean and median give unbiased estimates of the population mean. What criteria would you consider in choosing which statistic to use if you wanted to estimate the population mean?

The standard error of is .

Using an unbiased statistic guarantees that there will be no systematic tendency to under- or overestimate the value of the population characteristic and that estimates will almost always be relatively close to the true value.

What is the difference between an unbiased statistic and a biased statistic?

A 90% confidence interval for a population proportion calculated using data from a random sample of size n = 51 is (0.573, 0.787) . Which of the following is the 95% confidence interval calculated from the same data? ​

Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration: Which statistic would you recommend?

Chuck has decided to increase the size of the sample he uses to estimate a population proportion. ​ What is the effect on the width of the associated confidence interval? ​

An unbiased statistic is one that ​

The sampling distribution of p tends to be more spread out for larger sample sizes than for smaller sample sizes.

Jasmine has decided to decrease the confidence level in her estimation of a population proportion. What is the effect on the width of the associated confidence interval? ​ ​

Holding all other elements equal, an increase in sample size will result in a wider confidence interval.

A statistic that is unbiased with a small standard error is likely to result in an estimate that is close to the actual value of the population characteristic.

When choosing a statistic for computing an estimate, what factors should be considered?

To estimate the proportion of faculty at a state university who own a home, a random sample of faculty is selected. For which of the following combinations of n and would it be appropriate to use the confidence interval to estimate the population proportion? ​

Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95% confidence interval for the proportion that has Internet access is (0.73, 0.79) . Which of the following is a correct interpretation of the 95% confidence level? ​

All else being equal, the higher the confidence level, the wider the confidence interval.

A 90% confidence interval for a population proportion calculated using data from a random sample of size n = 51 is (0.573, 0.787) . Which of the following is the 95% confidence interval calculated from the same data?

Chuck has decided to increase the size of the sample he uses to estimate a population proportion. What is the effect on the width of the associated confidence interval?

An unbiased statistic is one that

Jasmine has decided to decrease the confidence level in her estimation of a population proportion. What is the effect on the width of the associated confidence interval?

To estimate the proportion of faculty at a state university who own a home, a random sample of faculty is selected. For which of the following combinations of n and would it be appropriate to use the confidence interval to estimate the population proportion?

Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95% confidence interval for the proportion that has Internet access is (0.73, 0.79) . Which of the following is a correct interpretation of the 95% confidence level?