Question 1

True or False: A sample size of 5 provides a sample mean of 9.6.If the population variance is
known to be 5 and the population distribution is assumed to be normal, the lower limit for a
90% confidence interval is 7.96.

Accepted Answer

The lower limit for a 90% confidence interval is calculated as the sample mean minus the critical value multiplied by the standard error of the mean. The critical value for a 90% confidence interval with a sample size of 5 is 2.262. The standard error of the mean is the population standard deviation divided by the square root of the sample size, which is 5 / sqrt(5) = 2.236. Therefore, the lower limit for the 90% confidence interval is 9.6 - 2.262 * 2.236 = 7.96.

Question 2

Accepted Answer

The answer of ...

Question 3

It is desired to estimate the mean total compensation of CEOs in the Service industry.Data
Were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be
($2,181,260, $5,836,180).Based on the interval above, do you believe the mean total
Compensation of CEOs in the Service industry is more than $3,000,000?

Accepted Answer

The confidence interval includes values both below and above $3,000,000, so we cannot be 95% confident that the mean exceeds $3,000,000.

Question 4

An economist is interested in studying the incomes of consumers in a particular country.The
Population standard deviation is known to be $1,000.A random sample of 50 individuals
Resulted in a mean income of $15,000.What is the upper end point in a 99% confidence
Interval for the average income?

Accepted Answer

The upper endpoint of a 99% confidence interval is calculated using the formula: mean + (Z * (σ/√n)). Here, Z for 99% confidence is approximately 2.576, σ is $1,000, and n is 50. Calculating gives $15,000 + (2.576 * (1000/√50)) = $15,364.

Question 5

Accepted Answer

The answer of ...

Question 6

True or False: The t distribution is used to construct confidence intervals for the population
mean when the population standard deviation is unknown.

Accepted Answer

The t distribution is used when the population standard deviation is unknown and the sample size is small, allowing for more accurate confidence intervals for the population mean.

Question 7

It is desired to estimate the mean total compensation of CEOs in the Service industry.Data
Were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be
($2,181,260, $5,836,180).Which of the following interpretations is correct?

Accepted Answer

The correct interpretation of a confidence interval is that we are 95% confident that the mean total compensation of all CEOs in the Service industry falls within the interval $2,181,260 to $5,836,180.

Question 8

Accepted Answer

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Question 9

A 99% confidence interval estimate can be interpreted to mean that

Accepted Answer

A 99% confidence interval means that if we were to take many samples and build a confidence interval from each, 99% of those intervals would contain the true population mean. It also means we are 99% confident that the interval calculated from our sample contains the true population mean.

Question 10

True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a
sample of 10 data points, a 90% confidence interval will have a width of 2.36.

Accepted Answer

The width of a confidence interval is calculated using the formula: CI width = 2 * Z * (σ/√n), where Z is the Z-score for the confidence level, σ is the population standard deviation, and n is the sample size. For a 90% confidence interval, Z is approximately 1.645. Plugging in the values, the width is not 2.36.

Question 11

An economist is interested in studying the incomes of consumers in a particular country.The
Population standard deviation is known to be $1,000.A random sample of 50 individuals
Resulted in a mean income of $15,000.What is the width of the 90% confidence interval?

Accepted Answer

The answer of An economist is interested in studying the...

Question 12

True or False: The difference between the sample mean and the population mean is called the
sampling error.

Accepted Answer

The answer of True or False: The difference between the...

Question 13

True or False: The t distribution is used to develop a confidence interval estimate of the
population mean when the population standard deviation is unknown.

Accepted Answer

The t distribution is used when the population standard deviation is unknown and the sample size is small, allowing for estimation of the population mean with a confidence interval.

Question 14

True or False: The confidence interval estimate of the population mean is constructed around
the sample mean.

Accepted Answer

The confidence interval for a population mean is calculated using the sample mean as the central point, with a margin of error added and subtracted to create the interval.

Question 15

True or False: The difference between the sample size and the population size is called the
sampling error.

Accepted Answer

The sampling error is the difference between a sample statistic and the corresponding population parameter, not the difference in size.

Question 16

The t distribution

Accepted Answer

The t distribution assumes the population is normally distributed, approaches the normal distribution as the sample size increases, and has more area in the tails compared to the normal distribution, especially with smaller sample sizes.

Question 17

If you were constructing a 99% confidence interval of the population mean based on a sample
Of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be

Accepted Answer

For a 99% confidence interval with n=25, degrees of freedom (df) = 24. The critical t-value for df=24 at 99% confidence is approximately 2.7969.

Question 18

True or False: The difference between the sample proportion and the population proportion is
called the sampling error.

Accepted Answer

The answer of True or False: The difference between the...

Question 19

Which of the following is not true about the Student's t distribution?

Accepted Answer

The Student's t distribution is used when the population standard deviation is unknown, not known.

Question 20

The t distribution approaches the standardized normal distribution when the number of
degrees of freedom increases.

Accepted Answer

As the number of degrees of freedom increases, the t distribution becomes more and more similar to the standard normal distribution. This is because the larger sample size associated with more degrees of freedom leads to a smaller standard error in the estimation of the population mean. As a result, the t statistic becomes closer to the z statistic, which follows the standard normal distribution.

Quiz 8: Confidence Interval Estimation

True or False: A sample size of 5 provides a sample mean of 9.6.If the population variance is known to be 5 and the population distribution is assumed to be normal, the lower limit for a 90% confidence interval is 7.96.

An economist is interested in studying the incomes of consumers in a particular country.The Population standard deviation is known to be $1,000.A random sample of 50 individuals Resulted in a mean income of $15,000.What is the upper end point in a 99% confidence Interval for the average income?

True or False: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

It is desired to estimate the mean total compensation of CEOs in the Service industry.Data Were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180) .Which of the following interpretations is correct?

A 99% confidence interval estimate can be interpreted to mean that

True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

An economist is interested in studying the incomes of consumers in a particular country.The Population standard deviation is known to be $1,000.A random sample of 50 individuals Resulted in a mean income of $15,000.What is the width of the 90% confidence interval?

True or False: The difference between the sample mean and the population mean is called the sampling error.

True or False: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

True or False: The confidence interval estimate of the population mean is constructed around the sample mean.

True or False: The difference between the sample size and the population size is called the sampling error.

The t distribution

If you were constructing a 99% confidence interval of the population mean based on a sample Of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be

True or False: The difference between the sample proportion and the population proportion is called the sampling error.

Which of the following is not true about the Student's t distribution?

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.