Question 1

A point estimator ₁ is said to be more efficient than a point estimator ₂ if Var( ₁)> Var( ₂).

Accepted Answer

The answer of A point estimator ₁ is said...

Question 2

A 95% confidence interval estimate for a population mean μ is determined to be 62.8 to 73.4.If the confidence level is reduced to 90%,the confidence interval for μ becomes narrower.

Accepted Answer

When the confidence level is reduced, the margin of error decreases, resulting in a narrower confidence interval. Therefore, the statement is true.

Question 3

The concept of margin of error is not applicable when estimating the population proportion P.

Accepted Answer

The concept of margin of error is applicable when estimating the population proportion P, as it is used to determine the range within which the true population proportion is likely to fall. The margin of error is a function of the sample size and the level of confidence used in the estimation.

Question 4

The sample proportion  
is a biased estimator of the population proportion P.

Accepted Answer

The answer of The sample proportion  
is a biased...

Question 5

In a recent survey of 574 employees,15.5% indicated that they were not in favor of a particular plan.What is the level of confidence associated with the interval of 12.85% to 19.89%?

Accepted Answer

The answer of In a recent survey of 574 employees,15.5%...

Question 6

The value of the standard error of the mean is determined by dividing the total error by the sample size.

Accepted Answer

The standard error of the mean is determined by dividing the standard deviation of the population (or sample) by the square root of the sample size. It is not determined by dividing the total error by the sample size.

Question 7

The bias of an unbiased estimator is equal to 1.

Accepted Answer

The bias of an unbiased estimator is 0, not 1. A bias of 1 would mean that the estimator consistently overestimates the true parameter value by 1 unit.

Question 8

You are told that a 95% confidence interval for the population mean is 17.3 to 24.5.If the population standard deviation is 18.2,how large was the sample?

Accepted Answer

The answer of You are told that a 95% confidence...

Question 9

A student records the time (in minutes)it takes to commute to school for seven days.Those results are: 21,15,13,16,10,13,and 18.Assuming the population is normally distributed,develop a 95% confidence interval for the population mean.

Accepted Answer

The answer of A student records the time (in minutes)it...

Question 10

The number of bolts produced each hour from a particular machine is normally distributed with a standard deviation of 7.4.For a random sample of 15 hours,the average number of bolts produced was 587.3.Find the upper and lower confidence limits of a 98% confidence interval for the population mean number of bolts produced per hour.

Accepted Answer

The answer of The number of bolts produced each hour...

Question 11

In a recent survey of 600 adults,16.4% indicated that they had fallen asleep in front of the television in the past month.Develop a 95% confidence interval for the population proportion.

Accepted Answer

The answer of In a recent survey of 600 adults,16.4%...

Question 12

The normal distribution is used to develop a confidence interval estimate of the population proportion if the sample size is large.

Accepted Answer

The normal distribution can be used to develop a confidence interval estimate of the population proportion if the sample size is large. This is because, according to the central limit theorem, for large sample sizes the sample proportion is approximately normally distributed.

Question 13

A narrower confidence interval for a population parameter with a given confidence level can be obtained by increasing the sample size.

Accepted Answer

This statement is true. Increasing the sample size will decrease the standard error and result in a narrower confidence interval for the same level of confidence.

Question 14

If the campaign manager of a US senator is interested in estimating the proportion of registered voters who will support the senator during the next election,the sample proportion  
would be the appropriate point estimate.

Accepted Answer

The sample proportion would be an appropriate point estimate for the proportion of registered voters who will support the senator during the next election.

Question 15

An unbiased estimation procedure for the population total Nμ yields the point estimate N  
.

Accepted Answer

The statement presents a point estimate for the population total Nμ and claims it to be unbiased. Without further information, we can assume that this statement is true.

Question 16

The amount of material used in making a custom sail for a sailboat is normally distributed.For a random sample of 15 sails,you find that the mean amount of material is 912 square feet,with a standard deviation of 64 square feet.Develop a 99% confidence interval for the population mean amount of material used in a custom sail.

Accepted Answer

The answer of The amount of material used in making...

Question 17

You are interested in determining the amount of time (in minutes)you spend each day on the Internet.For seven days,these values are: 51,24,16,88,63,28,and 59.Assume that the amount of time you spend on the Internet each day is normally distributed,and develop a 90% confidence interval for the population average amount of time.

Accepted Answer

The answer of You are interested in determining the amount...

Question 18

Whatever the value of the sample proportion,  
(1 -  
)cannot be smaller than 0.25.

Accepted Answer

The answer of Whatever the value of the sample proportion,...

Question 19

The maximum distance between an estimator and the true value of a parameter is called the margin of error.

Accepted Answer

This is a correct statement about the margin of error in statistics.

Question 20

A 95% confidence interval for the population proportion will not extend approximately 1.96  
on each side of the sample proportion.

Accepted Answer

The answer of A 95% confidence interval for the population...

Quiz 7: Estimation: Single Population

A point estimator 1 is said to be more efficient than a point estimator 2 if Var( 1)> Var( 2).