Question 1

As the number of degrees of freedom for a t-distribution increases:

Accepted Answer

A) the dispersion of the distribution decreases. 
B) the shape of the distribution becomes narrower and taller. 
C) the t-distribution becomes more and more similar to the standard normal distribution. 
D) All of these choices are correct. 
A) the dispersion of the distribution decreases. 
B) the shape of the distribution becomes narrower and taller. 
C) the t-distribution becomes more and more similar to the standard normal distribution. 
D) All of these choices are correct.

Question 2

A statistician wants to estimate the mean weekly family expenditure on clothes. He believes that the largest weekly expenditure is $650 and the lowest is $150.
a. Estimate the standard deviation of the weekly expenditure.
b. Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

Accepted Answer

a. s F1F1F1S1F1F1F1

Question 3

We cannot interpret the confidence interval estimate of ? as a probability statement about ? , simply because the population mean is a fixed but unknown quantity.

Accepted Answer

A) True 
 B)False

Question 4

The objective of estimation is to determine the approximate value of:

Accepted Answer

A) a sample statistic. 
B) a population parameter. 
C) the sample mean. 
D) the sample variance. 
A) a sample statistic. 
B) a population parameter. 
C) the sample mean. 
D) the sample variance.

Question 5

The nighttime temperature readings for 20 winter days in Sydney are normally distributed with a mean of 5.5ºC and a population standard deviation of 1.5ºC. Determine the 90% confidence interval estimate for the mean winter nighttime temperature.

Accepted Answer

4.9483ºC t

Question 6

Which of the following assumptions must be true in order to use the formula $$\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$$ to find a confidence interval estimate of the population mean?

Accepted Answer

A) The population variance is known. 
B) The population mean is known. 
C) The population is normally distributed. 
D) The confidence level is greater than 90%. 
A) The population variance is known. 
B) The population mean is known. 
C) The population is normally distributed. 
D) The confidence level is greater than 90%.

Question 7

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

Accepted Answer

The answer of Determine the sample size that is required...

Question 8

How large a sample must be drawn to estimate a population proportion to within 0.03 with 95% confidence if we believe that the proportion lies somewhere between 25% and 45%?

Accepted Answer

The answer of How large a sample must be drawn...

Question 9

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours.
Determine the 95% confidence interval estimate of the population mean, changing the sample size to 300.

Accepted Answer

6.3303 to

Question 10

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours.
Determine the 95% confidence interval estimate of the population mean, changing the sample size to 36.

Accepted Answer

The answer of Suppose that the amount of time teenagers...

Question 11

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $$\hat { p }$$ , we:

Accepted Answer

A) take another sample and estimate p. 
B) take two more samples and find the average of their $$\hat { p }$$ values. 
C) let $$\hat { p }$$ = 0.50. 
D) let $$\hat { p }$$ = 0.95. 
A) take another sample and estimate p. 
B) take two more samples and find the average of their $$\hat { p }$$ values. 
C) let $$\hat { p }$$ = 0.50. 
D) let $$\hat { p }$$ = 0.95.

Question 12

A 90% confidence interval estimate of the population mean F1F1F1S1?F1F1F10 can be interpreted to mean that:

Accepted Answer

A) if we repeatedly draw samples of the same size from the same population, 90% of the values of the sample means $$\bar { x }$$ will result in a confidence interval that includes the population mean F1F1F1S1?F1F1F10. 
B) there is a 90% probability that the population mean F1F1F1S1?F1F1F10 will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). 
C) we are 90% confident that we have selected a sample whose range of values does not contain the population mean F1F1F1S1?F1F1F10. 
D) We are 90% confident that 10% the values of the sample means $$\bar { x }$$ will result in a confidence interval that includes the population mean F1F1F1S1?F1F1F10. 
A) if we repeatedly draw samples of the same size from the same population, 90% of the values of the sample means $$\bar { x }$$ will result in a confidence interval that includes the population mean F1F1F1S1?F1F1F10. 
B) there is a 90% probability that the population mean F1F1F1S1?F1F1F10 will lie between the lower confidence limit (LCL) and the upper confidence limit (UCL). 
C) we are 90% confident that we have selected a sample whose range of values does not contain the population mean F1F1F1S1?F1F1F10. 
D) We are 90% confident that 10% the values of the sample means $$\bar { x }$$ will result in a confidence interval that includes the population mean F1F1F1S1?F1F1F10.

Question 13

In an effort to identify the true proportion of first-year university students who are under 18 years of age, a random sample of 500 first-year students was taken. Only 50 of them were under the age of 18. The value 0.10 would be used as a point estimate to the true proportion of first-year students aged under 18.

Accepted Answer

A) True 
 B)False

Question 14

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

Accepted Answer

The answer of A survey of 100 retailers revealed that...

Question 15

The percentage of the confidence interval relies on the significance level.F1F1F1S1F1F1F10

Accepted Answer

A) True 
 B)False

Question 16

The problem with relying on a point estimate of a population parameter is that:

Accepted Answer

A) it has no variance. 
B) it might be unbiased. 
C) it might not be relatively efficient. 
D) it does not tell us how close or far the point estimate might be from the parameter. 
A) it has no variance. 
B) it might be unbiased. 
C) it might not be relatively efficient. 
D) it does not tell us how close or far the point estimate might be from the parameter.

Question 17

The width of the confidence interval estimate of the population mean ? is a function of only two quantities, the population standard deviation F1F1F1S1?F1F1F10 and the sample size n.

Accepted Answer

A) True 
 B)False

Question 18

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

In developing an interval estimate for a population mean, the population standard deviation $$\sigma$$ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had F1F1F1S1?F1F1F10 equalled 16, the interval estimate would have been 100 ± 5.0.

Accepted Answer

A) True 
 B)False

As the number of degrees of freedom for a t-distribution increases:

We cannot interpret the confidence interval estimate of ? as a probability statement about ? , simply because the population mean is a fixed but unknown quantity.

The objective of estimation is to determine the approximate value of:

The nighttime temperature readings for 20 winter days in Sydney are normally distributed with a mean of 5.5ºC and a population standard deviation of 1.5ºC. Determine the 90% confidence interval estimate for the mean winter nighttime temperature.

Which of the following assumptions must be true in order to use the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ to find a confidence interval estimate of the population mean?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

How large a sample must be drawn to estimate a population proportion to within 0.03 with 95% confidence if we believe that the proportion lies somewhere between 25% and 45%?

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $\hat { p }$ , we:

A 90% confidence interval estimate of the population mean ? can be interpreted to mean that:

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

The percentage of the confidence interval relies on the significance level.

The problem with relying on a point estimate of a population parameter is that:

The width of the confidence interval estimate of the population mean ? is a function of only two quantities, the population standard deviation ? and the sample size n.

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

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

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had ? equalled 16, the interval estimate would have been 100 ± 5.0.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 10: Estimation: Describing a Single Population

As the number of degrees of freedom for a t-distribution increases:

We cannot interpret the confidence interval estimate of ? as a probability statement about ? , simply because the population mean is a fixed but unknown quantity.

The objective of estimation is to determine the approximate value of:

The nighttime temperature readings for 20 winter days in Sydney are normally distributed with a mean of 5.5ºC and a population standard deviation of 1.5ºC. Determine the 90% confidence interval estimate for the mean winter nighttime temperature.

Which of the following assumptions must be true in order to use the formula Xˉ±za/2(σ/n)\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )Xˉ±za/2​(σ/n​) to find a confidence interval estimate of the population mean?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

How large a sample must be drawn to estimate a population proportion to within 0.03 with 95% confidence if we believe that the proportion lies somewhere between 25% and 45%?

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion p^\hat { p }p^​ , we:

A 90% confidence interval estimate of the population mean ? can be interpreted to mean that:

A survey of 100 retailers revealed that the mean after-tax profit was $80 000. Assuming that the population standard deviation is $15 000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

The percentage of the confidence interval relies on the significance level.

The problem with relying on a point estimate of a population parameter is that:

The width of the confidence interval estimate of the population mean ? is a function of only two quantities, the population standard deviation ? and the sample size n.

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

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

In developing an interval estimate for a population mean, the population standard deviation σ\sigmaσ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had ? equalled 16, the interval estimate would have been 100 ± 5.0.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Which of the following assumptions must be true in order to use the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ to find a confidence interval estimate of the population mean?

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion $\hat { p }$ , we:

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 8. The interval estimate was 50.0 ± 2.50. Had ? equalled 16, the interval estimate would have been 100 ± 5.0.