Question 1

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70.
What sample size should you use?

Accepted Answer

The answer of Suppose that your task is to estimate...

Question 2

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 90% confidence interval estimate of the population mean.

Accepted Answer

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

Question 3

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

Accepted Answer

A)  A non-normal population with a large sample and an unknown population variance. 
B)  A normal population with a large sample and a known population variance. 
C)  A non-normal population with a small sample and an unknown population variance. 
D)  A normal population with a small sample and an unknown population variance.

Question 4

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

Accepted Answer

A)  77.769. 
B)  72.231. 
C)  72.727. 
D)  77.273.

Question 5

The difference between the sample statistic and actual value of the population parameter is the percentage of the confidence interval.

Accepted Answer

A) True 
 B)False

Question 6

Which of the following assumptions must be true in order to use the formula $\bar { x } \pm z _ { \mathfrak { w } / 2 } \sigma / \sqrt { n }$ 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%.

Question 7

A politician believes that the proportion of voters who will vote for a Coalition candidate in the 2004 general election is 0.65. A sample of 500 voters is selected at random.
a. Assume that the politician is correct and p = 0.65. What is the sampling distribution of the sample proportion $\hat { p }$ ? Explain.
b. Find the expected value and standard deviation of the sample proportion $\hat { p }$ .
c. What is the probability that the number of voters in the sample who will vote for a Labor candidate in the 2004 general election will be between 340 and 350?

Accepted Answer

The answer of A politician believes that the proportion of...

Question 8

A 90% confidence interval estimate of the population mean$\mu$ 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 $\mu$. 
B)  there is a 90% probability that the population mean $\mu$ 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 $\mu$. 
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$\mu$.

Question 9

Determine the minimum sample size required for estimating the population proportion of number of people who drive to work, to within 0.003, with 80% confidence.

Accepted Answer

The answer of Determine the minimum sample size required for...

Question 10

The upper limit of the 90% confidence interval for $\mu$ , given that n = 64, $\bar { x }$ = 70 and $\sigma$ = 20, is 65.89.

Accepted Answer

A) True 
 B)False

Question 11

A random sample of 10 waitresses in Darwin revealed the following hourly earnings (in dollars, including tips): $$\begin{array} { | r | r | r | r | r | r | r | r | r | r | } 
\hline 19 & 18 & 15 & 16 & 18 & 17 & 16 & 18 & 20 & 14 \
\hline
\end{array}$$ If the hourly earnings are normally distributed with a standard deviation of $4.5, estimate with 95% confidence the mean hourly earnings for all waitresses in Darwin.

Accepted Answer

The answer of A random sample of 10 waitresses in...

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

Accepted Answer

A)  Student t distribution 
B)  Standard normal distribution 
C)  Chi-square distribution 
D)  None of these choices are correct.

Question 14

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been:

Accepted Answer

A)  60.92 ± 2.14. 
B)  50.92 ± 12.14. 
C)  101.84 ± 4.28. 
D)  50.92 ± 4.28.

Question 15

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.
Interpret what the confidence interval estimate tells you.

Accepted Answer

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

Question 16

When constructing a confidence interval estimate of $\mu$ , doubling the sample size n reduces the width %of the interval by half.

Accepted Answer

A) True 
 B)False

Question 17

A robust estimator is one that:

Accepted Answer

A)  is unbiased and symmetrical about zero. 
B)  is consistent and is also mound-shaped. 
C)  is efficient and less spread out. 
D)  is not sensitive to moderate departure from the assumption of normality in the population.

Question 18

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

The answer of A statistician wants to estimate the mean...

Question 19

Which of the following statements is (are) correct?

Accepted Answer

A)  The sample mean is a biased estimator of the population mean. 
B)  The sample proportion is an unbiased estimator of the population proportion. 
C)  The sample mean is not a consistent estimator. 
D)  All of these choices are correct.

Question 20

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

Accepted Answer

A) True 
 B)False

Exam 11: Estimation: Describing a Single Population

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use?

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 90% confidence interval estimate of the population mean.

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The difference between the sample statistic and actual value of the population parameter is the percentage of the confidence interval.

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

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

Determine the minimum sample size required for estimating the population proportion of number of people who drive to work, to within 0.003, with 80% confidence.

The upper limit of the 90% confidence interval for $\mu$ , given that n = 64, $\bar { x }$ = 70 and $\sigma$ = 20, is 65.89.

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

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been:

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. Interpret what the confidence interval estimate tells you.

When constructing a confidence interval estimate of $\mu$ , doubling the sample size n reduces the width %of the interval by half.

A robust estimator is one that:

Which of the following statements is (are) correct?

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

Exam 11: Estimation: Describing a Single Population

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use?

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 90% confidence interval estimate of the population mean.

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The difference between the sample statistic and actual value of the population parameter is the percentage of the confidence interval.

Which of the following assumptions must be true in order to use the formula xˉ±zw/2σ/n\bar { x } \pm z _ { \mathfrak { w } / 2 } \sigma / \sqrt { n }xˉ±zw/2​σ/n​ to find a confidence interval estimate of the population mean?

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

Determine the minimum sample size required for estimating the population proportion of number of people who drive to work, to within 0.003, with 80% confidence.

The upper limit of the 90% confidence interval for μ\muμ , given that n = 64, xˉ\bar { x }xˉ = 70 and σ\sigmaσ = 20, is 65.89.

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

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

In developing an interval estimate for a population mean, the population standard deviation σ\sigmaσ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had σ\sigmaσ equaled 20, the interval estimate would have been:

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. Interpret what the confidence interval estimate tells you.

When constructing a confidence interval estimate of μ\muμ , doubling the sample size n reduces the width %of the interval by half.

A robust estimator is one that:

Which of the following statements is (are) correct?

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.

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

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

The upper limit of the 90% confidence interval for $\mu$ , given that n = 64, $\bar { x }$ = 70 and $\sigma$ = 20, is 65.89.

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

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been:

When constructing a confidence interval estimate of $\mu$ , doubling the sample size n reduces the width %of the interval by half.