Question 1

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 2

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

Increasing the planning value p* to .5 actually increases the margin of error because it maximizes the standard error, rather than reducing it.

Question 3

​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, as the margin of error is about the precision of the estimate rather than its central value.

Question 4

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 p (the population proportion) is not recommended because it suggests a population proportion of 100%, which is unrealistic for most practical situations. Instead, using a sample proportion from a previous study, a preliminary sample, or a judgment/best guess are more appropriate methods for estimating p when it is unknown.

Question 5

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 approaches the normal distribution. This is because the t distribution is based on sample size (degrees of freedom), and as the sample size increases, the t distribution becomes more similar to the standard normal distribution.

Question 6

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 calculated based on the sample size. Therefore, choice C is the correct answer. The other choices are not related to the t distribution.

Question 7

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

Using .5 as an estimate is not a recommended procedure for estimating the population standard deviation when σ is unknown.

Question 8

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 distribution assuming it is symmetric around zero.

Question 9

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 equal to (1 - confidence coefficient). This value typically ranges from 0.01 to 0.10, and represents the maximum probability of mistakenly rejecting the null hypothesis. It cannot be a negative value, nor can it be any arbitrary positive value. It is also not within the range of -1.96 to 1.96, which is the range of values for the standard normal distribution at the 95% confidence level.

Question 10

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 in a confidence interval estimate is calculated as follows: ME=z*σ/√n, where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. Since z and σ are constants for a given confidence level, the margin of error will be the same for all samples of the same size.

Question 11

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 12

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 t distribution is used when the sample standard deviation is used to estimate the population standard deviation, especially with small sample sizes.

Question 13

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 standard error of the mean is calculated using the formula: SE = σ / √n, where σ is the standard deviation and n is the sample size. Here, SE = 20 / √100,000 = 0.0632.

Question 14

​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 consists of a point estimate (such as a sample mean or sample proportion) plus and minus a margin of error. This margin of error represents the degree of uncertainty in the estimate and is often determined by the confidence level desired for the estimate. Therefore, the correct option is C, which identifies "point estimate, margin of error" as the terms involved in an interval estimate.

Question 15

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 needed to estimate a population proportion with a specified margin of error is maximized when the planning value of p (the estimated proportion) is .50. This is because the formula for calculating sample size in this context includes the term p(1-p), which reaches its maximum value when p = .50, thus requiring the largest sample size to ensure the margin of error is met.

Question 16

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 solely based on the sample size (n). This means that as the sample size increases, the degrees of freedom increase and the t distribution approaches a normal distribution. The other choices listed (area in the upper tail, sample standard deviation, and confidence coefficient) do not affect the degrees of freedom.

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 required for computing the minimum sample size for an interval estimate of μ. The necessary inputs are the desired margin of error, confidence level, and either the population standard deviation or an estimate of it from a previous sample.

Question 18

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 of the mean and proportion decreases, which leads to narrower confidence intervals. This is because a larger sample size provides more information about the population, resulting in a more accurate estimate of the population parameter.

Question 19

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 represents the likelihood of making a Type I error, where the true parameter lies outside the confidence interval constructed.

Question 20

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

We can use the formula for margin of error:

ME = z* (σ / sqrt(n))

where ME is the margin of error, z* is the critical value for the confidence level (in this case, 95% confidence corresponds to z*=1.96), σ is the population standard deviation (which we don't know, but we have the population variance, so we can take the square root to get σ=√125=11.18), and n is the sample size we want to determine.

We want the margin of error to be at most 3, so we can set up the following inequality:

3 ≤ 1.96* (11.18 / sqrt(n))

Solving for n, we get:

n ≥ (1.96*11.18 / 3)² = 53.79

Since we need a whole number for the sample size, we round up to the nearest integer and get n=54.

Therefore, the best choice is C) 54 because it is the smallest sample size that satisfies the requirements.

Quiz 8: Interval Estimation

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?

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

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

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

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

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

The level of significance α

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

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

The t distribution should be used whenever the

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.

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

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

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

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

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

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

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?

Quiz 8: Interval Estimation

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?

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

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

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​

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

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