Question 1

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

Accepted Answer

A) True 
 B)False  True

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 95% confidence interval estimate of the population mean, changing the sample mean to 5.0 hours.

Accepted Answer

4.706 to 5.294.

Question 3

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 to 6.0517ºC.

Question 4

The sample proportion $\hat { p }$ is a consistent estimator of the population proportion p because it is unbiased and the variance of $\hat { p }$ is p(1 - p)/n, which grows smaller as n grows larger.

Accepted Answer

A) True 
 B)False

Question 5

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

Accepted Answer

A) True 
 B)False

Question 6

You need four values to construct the confidence interval estimate of $\mu$ . These are the sample mean, sample size, population standard deviation and confidence level.

Accepted Answer

A) True 
 B)False

Question 7

Recall the rule of thumb used to indicate when the normal distribution is a good approximation to the sampling distribution for the sample proportion $\hat { p }$ . For the combination n = 50; p = 0.05, the rule is satisfied.

Accepted Answer

A) True 
 B)False

Question 8

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

Accepted Answer

A)   0.0274.
B)   0.50.
C)   0.0316.
D)   0.0548.

Question 9

A confidence interval is defined as:

Accepted Answer

A)   a point estimate plus or minus a specific level of confidence.
B)   a lower and upper confidence limit associated with a specific level of confidence.
C)   an interval that has a 95% probability of containing the population parameter.
D)   a lower and upper confidence limit that has a 95% probability of containing the population parameter.

Question 10

The population proportion of voters in favour of a particular political candidate is being estimated with a confidence interval. A random sample of 55 voters is taken, and 28 are found to be in favour. Find and interpret a 90% confidence interval for the population proportion of people in favour of this political candidate.

Accepted Answer

The answer of The population proportion of voters in favour...

Question 11

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }$

Accepted Answer

A)   The sample size is greater than 30.
B)   The population variance is known.
C)   The population is normal.
D)   The sample is drawn from a positively skewed distribution.

Question 12

Which of the following statements are correct?

Accepted Answer

A)   If there are two unbiased estimators of a parameter, the one whose variance is larger is said to be relatively efficient.
B)   If there are two unbiased estimators of a parameter, the one whose mean is larger is said to be relatively efficient.
C)   If there are two unbiased estimators of a parameter, the one whose mean is smaller is said to be relatively efficient.
D)   If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

Question 13

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of:

Accepted Answer

A)   z = 1.96.
B)   z = 1.645.
C)   t = 2.045.
D)   t = 1.699.

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

A sample of size 300 is to be taken at random from an infinite population. Given that the population proportion is 0.70, the probability that the sample proportion will be smaller than 0.75 is:

Accepted Answer

A)   0.9706.
B)   0.4772.
C)   0.4706.
D)   0.9772.

Question 16

At a given sample size and level of confidence, the smaller the population standard deviation $\sigma$ , the wider and thus the less precise the confidence interval estimate of $\mu$ is.

Accepted Answer

A) True 
 B)False

Question 17

When constructing confidence interval for a parameter, we generally set the confidence level $1 - \alpha$ close to 1 (usually between 0.90 and 0.99) because we would like to be reasonably confident that the interval includes the actual value of the population parameter.

Accepted Answer

A) True 
 B)False

Question 18

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 population standard deviation to 1.2.

Accepted Answer

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

Question 19

The lower and upper limits of the 68.26% confidence interval for the population mean $\mu$ , given that n = 64, $\bar { x }$ = 110 and $\sigma$ = 8, are 109 and 111, respectively.

Accepted Answer

A) True 
 B)False

Question 20

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 mean to 8.5 hours.

Accepted Answer

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

Exam 11: Estimation: Describing a Single Population

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

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.

The sample proportion p^\hat { p }p^​ is a consistent estimator of the population proportion p because it is unbiased and the variance of p^\hat { p }p^​ is p(1 - p)/n, which grows smaller as n grows larger.

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

You need four values to construct the confidence interval estimate of μ\muμ . These are the sample mean, sample size, population standard deviation and confidence level.

Recall the rule of thumb used to indicate when the normal distribution is a good approximation to the sampling distribution for the sample proportion p^\hat { p }p^​ . For the combination n = 50; p = 0.05, the rule is satisfied.

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

A confidence interval is defined as:

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? xˉ±tn/2sn\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }xˉ±tn/2​n​s​

Which of the following statements are correct?

For a sample of size 30 taken from a normally distributed population with standard deviation equal to 5, a 95% confidence interval for the population mean would require the use of:

The width of the confidence interval estimate of the population mean μ\muμ is a function of only two quantities, the population standard deviation σ\sigmaσ and the sample size n.

A sample of size 300 is to be taken at random from an infinite population. Given that the population proportion is 0.70, the probability that the sample proportion will be smaller than 0.75 is:

At a given sample size and level of confidence, the smaller the population standard deviation σ\sigmaσ , the wider and thus the less precise the confidence interval estimate of μ\muμ is.

When constructing confidence interval for a parameter, we generally set the confidence level 1−α1 - \alpha1−α close to 1 (usually between 0.90 and 0.99) because we would like to be reasonably confident that the interval includes the actual value of the population parameter.

The lower and upper limits of the 68.26% confidence interval for the population mean μ\muμ , given that n = 64, xˉ\bar { x }xˉ = 110 and σ\sigmaσ = 8, are 109 and 111, respectively.

The sample proportion $\hat { p }$ is a consistent estimator of the population proportion p because it is unbiased and the variance of $\hat { p }$ is p(1 - p)/n, which grows smaller as n grows larger.

You need four values to construct the confidence interval estimate of $\mu$ . These are the sample mean, sample size, population standard deviation and confidence level.

Recall the rule of thumb used to indicate when the normal distribution is a good approximation to the sampling distribution for the sample proportion $\hat { p }$ . For the combination n = 50; p = 0.05, the rule is satisfied.

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }$

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

At a given sample size and level of confidence, the smaller the population standard deviation $\sigma$ , the wider and thus the less precise the confidence interval estimate of $\mu$ is.

When constructing confidence interval for a parameter, we generally set the confidence level $1 - \alpha$ close to 1 (usually between 0.90 and 0.99) because we would like to be reasonably confident that the interval includes the actual value of the population parameter.

The lower and upper limits of the 68.26% confidence interval for the population mean $\mu$ , given that n = 64, $\bar { x }$ = 110 and $\sigma$ = 8, are 109 and 111, respectively.