Question 1

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.Determine the standard error of the mean.
A) .0632
B) .0002
C) 20.00
D) .0141

Accepted Answer

The answer of A random sample of 100,000 credit sales...

Question 2

As the degrees of freedom increase, the t distribution approaches the _____ distribution.
A) uniform
B) normal
C) exponential
D) p

Accepted Answer

As the degrees of freedom increase, the t distribution increasingly resembles the normal distribution. This is because the t distribution is derived from the normal distribution, and as the sample size (and degrees of freedom) increase, the sample mean approaches the population mean, and the sample standard deviation approaches the population standard deviation, making the distribution more and more normal.

Question 3

​The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.
A) ​population mean, standard error
B) population proportion, standard error
C) ​point estimate, margin of error
D) ​planning value, confidence coefficient

Accepted Answer

An interval estimate of a population mean or a population proportion is composed of two parts: a point estimate and a margin of error. The point estimate is the best estimate of the population parameter and the margin of error accounts for the variability and uncertainty in the estimate. The general form of the interval estimate is point estimate plus and minus the margin of error. Therefore, C is the correct choice. A is incorrect because it only applies to the interval estimate of a population mean, not a population proportion. B is incorrect because it only applies to the interval estimate of a population proportion, not a population mean. D is incorrect because it is not a commonly used term in statistics.

Question 4

The mean of the t distribution is​
A) ​0.
B) ​.5.
C) ​1.
D) ​problem specific.

Accepted Answer

The mean of the t distribution is 0, which is a property of the t distribution, indicating that it is symmetric around zero.

Question 5

The t distribution should be used whenever the
A) sample size is less than 30.
B) sample standard deviation is used to estimate the population standard deviation.
C) population is not normally distributed.
D) population standard deviation is known.

Accepted Answer

The answer of The t distribution should be used whenever...

Question 6

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except​
A) ​use the estimated σ from a previous study.
B) ​use the sample standard deviation from a preliminary sample.
C) ​use judgment or a best guess.
D) use .5 as an estimate.

Accepted Answer

The answer of To compute the necessary sample size for...

Question 7

The use of the normal probability distribution as an approximation of the sampling distribution of  is based on the condition that both np and n(1 - p) equal or exceed​
A) ​.05.
B) ​5.
C) ​10.
D) ​30.

Accepted Answer

The answer of The use of the normal probability distribution...

Question 8

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor.What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?
A) 625
B) 626
C) 600
D) 601

Accepted Answer

The answer of We are interested in conducting a study...

Question 9

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate
A) ​varies from sample to sample of the same size.
B) ​is the same for all samples of the same size.
C) ​increases as the sample size increases.
D) ​is independent of sample size.

Accepted Answer

When σ is known, the margin of error is based on the sample size and the confidence level, and is independent of the population size or variability. Therefore, the margin of error would be the same for all samples of the same size and the same confidence level.

Question 10

Confidence intervals for the population mean µ and population proportion p _____ as the size of the sample increases.
A) become narrower
B) become wider
C) remain the same
D) get closer to 1.

Accepted Answer

As the sample size increases, the standard error decreases, which results in a narrower confidence interval. This is because a larger sample size reduces the variability and uncertainty of the sample mean or proportion, allowing us to estimate the population parameter with greater precision and confidence.

Question 11

The level of significance α
A) can be any positive value.
B) is always a negative value.
C) is (1 - confidence coefficient).
D) can be any value between -1.96 to 1.96.

Accepted Answer

The level of significance α is equivalent to the probability of making a Type I error, which is rejecting a true null hypothesis. It is typically set at 0.05 or 0.01, which corresponds to a confidence coefficient of 95% or 99%. Therefore, α = (1 - confidence coefficient). Option A is incorrect because α must be a positive value. Option B is incorrect because α cannot be negative. Option D is incorrect because the range of values -1.96 to 1.96 corresponds to the 95% confidence interval for a standard normal distribution, not the level of significance.

Question 12

The degrees of freedom associated with a t distribution are a function of the​
A) ​area in the upper tail.
B) ​sample standard deviation.
C) ​confidence coefficient.
D) ​sample size.

Accepted Answer

The degrees of freedom associated with a t distribution are a function of the sample size. Specifically, for a t distribution, the degrees of freedom equal the sample size minus one.

Question 13

We can reduce the margin of error in an interval estimate of p by doing any of the following except​
A) ​increasing the sample size.
B) ​increasing the planning value p* to .5.
C) ​increasing α.
D) ​reducing the confidence coefficient.

Accepted Answer

The answer of We can reduce the margin of error...

Question 14

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the​
A) proportion estimate.
B) ​margin of error.
C) ​confidence coefficient.
D) same as α.

Accepted Answer

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter is the same as the significance level, denoted by α. This is because the confidence level (1 - α) represents the proportion of times the confidence interval would contain the true parameter if the procedure were repeated many times, so α represents the proportion of times it would not.

Question 15

​The margin of error in an interval estimate of the population mean is a function of all of the following except
A) α.
B) ​sample mean.
C) ​sample size.
D) ​variability of the population.

Accepted Answer

The margin of error in an interval estimate of the population mean depends on the level of confidence (related to α), the sample size, and the variability of the population. It does not directly depend on the sample mean itself.

Question 16

The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to​
A) ​.01.
B) ​.50.
C) ​.51.
D) ​.99.

Accepted Answer

The sample size required to estimate a population proportion with a specific margin of error is maximized when the planning value of p (the estimated proportion) is 0.50. This is because the formula for calculating sample size involves the term p(1-p), which reaches its maximum value when p = 0.50, thus requiring the largest sample size to meet the margin of error requirement.

Question 17

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except
A) desired margin of error.
B) confidence level.
C) population standard deviation.
D) degrees of freedom.

Accepted Answer

Degrees of freedom are not necessary for computing the minimum sample size for an interval estimate of μ. The minimum sample size can be calculated using the formula n = (z*σ/E)^2, where n is the sample size, z* is the critical value of the standard normal distribution corresponding to the desired confidence level, σ is the population standard deviation, and E is the desired margin of error.

Question 18

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the​
A) ​finite correction factor.
B) ​sample size.
C) ​degrees of freedom.
D) ​standard deviation.

Accepted Answer

The t distribution depends on the degrees of freedom, which is determined by the sample size. The other options are not directly related to the t distribution.

Question 19

It is known that the population variance (σ²) is 125.At 95% confidence, what sample size should be taken so that the margin of error does not exceed 3? A) 52 B) 53 C) 54 D) 55

Accepted Answer

The formula for calculating the margin of error is:

ME = z* (σ/√n)

where ME is the margin of error, z* is the critical value for the desired level of confidence (in this case, 1.96 for 95% confidence), σ is the population standard deviation (which can be calculated as the square root of the population variance, so σ=√125=11.18), and n is the sample size.

We want to find the sample size (n) that will give us a margin of error (ME) of no more than 3. So we can rearrange the formula to solve for n:

n = (z*/ME)^2 * σ^2

Plugging in the values we know:

n = (1.96/3)^2 * 125
n = 54.01

Since we can't have a fractional sample size, we must round up to the nearest whole number, giving us a sample size of 54.

Therefore, the best choice is (C) 54.

Question 20

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except​
A) ​use the sample proportion from a previous study.
B) ​use the sample proportion from a preliminary sample.
C) ​use 1.0 as an estimate.
D) ​use judgment or a best guess.

Accepted Answer

Using 1.0 as an estimate for a population proportion is not recommended because it does not provide a realistic estimate of variability in the population. The most conservative estimate when p is unknown is 0.5, as it maximizes the sample size required for a given level of precision.

Quiz 8: Interval Estimation

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.Determine the standard error of the mean.

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

The general form of an interval estimate of a population mean or a population proportion is the _ plus and minus the _.

The mean of the t distribution is

The t distribution should be used whenever the

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor.What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

Confidence intervals for the population mean µ and population proportion p _____ as the size of the sample increases.

The level of significance α

The degrees of freedom associated with a t distribution are a function of the

We can reduce the margin of error in an interval estimate of p by doing any of the following except

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

The margin of error in an interval estimate of the population mean is a function of all of the following except

The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

It is known that the population variance (σ²) is 125.At 95% confidence, what sample size should be taken so that the margin of error does not exceed 3?

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except

Quiz 8: Interval Estimation

A random sample of 100,000 credit sales in a department store showed an average sale of $87.25.From past data, it is known that the standard deviation of the population is $20.00.Determine the standard error of the mean.

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

​The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.

The mean of the t distribution is​

The t distribution should be used whenever the

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except​

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed​

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor.What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

Confidence intervals for the population mean µ and population proportion p _____ as the size of the sample increases.

The level of significance α

The degrees of freedom associated with a t distribution are a function of the​

We can reduce the margin of error in an interval estimate of p by doing any of the following except​

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the​

​The margin of error in an interval estimate of the population mean is a function of all of the following except

The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to​