Question 1

The z value associated with a two-sided 90% confidence interval is ___.
A)1.28
B)1.645
C)1.96
D)2.575
E)2.33

Accepted Answer

B

Question 2

Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers.Accordingly, his staff recorded the waiting times for 45 randomly selected walk-in customers, and calculated that their mean waiting time was 15 minutes.If Brian concludes that the average waiting time for all walk-in customers is 15 minutes, he is using a ___.
A)a range estimate
B)a statistical parameter
C)an interval estimate
D)a point estimate
E)an exact estimate

Accepted Answer

If Brian concludes that the average waiting time for all walk-in customers is 15 minutes, he is using a point estimate, which is an estimate of a population parameter based on a single value or point in a sample. It is not an interval estimate, which gives a range of values likely to contain the true population parameter, or a statistical parameter, which is a summary measure of a population. A range estimate and an exact estimate are not commonly used terms in statistics. Brian is using a point estimate because he is using the mean waiting time of the 45 randomly selected walk-in customers as an estimate for the average waiting time for all walk-in customers.

Question 3

When the population standard deviation, σ, is unknown the sample standard deviation, s, is used in determining the interval estimate for the population mean.

Accepted Answer

When the population standard deviation is unknown, the sample standard deviation is used in the calculation of the standard error and the t-distribution is used in determining the interval estimate for the population mean. When the population standard deviation is unknown, we use the sample standard deviation to estimate it in order to determine the interval estimate for the population mean.

Question 4

When a statistic calculated from sample data is used to estimate a population parameter, it is called a point estimate.

Accepted Answer

This is the definition of a point estimate. A point estimate is a single value (or point) used to estimate a population parameter based on sample data.

Question 5

If the population is normal and its standard deviation, σ, is known but the sample size is small, z-distribution values may not be used to determine interval estimates for the population mean.

Accepted Answer

When the population is normal and the standard deviation is known, z-distribution values can be used to determine interval estimates for the population mean regardless of the sample size.

Question 6

A t distribution is similar to a normal distribution, but flatter in the middle.

Accepted Answer

A t distribution has more area in the tails and less in the center compared to a normal distribution, which makes it flatter in the middle. This is because t distributions have more variability due to smaller sample sizes and the use of sample standard deviation instead of population standard deviation.

Question 7

Like a t distribution, a chi-square distribution is symmetrical and extends from minus infinity to plus infinity.

Accepted Answer

A chi-square distribution is not symmetrical and only extends from 0 to plus infinity. A chi-square distribution is not symmetrical and only extends from 0 to plus infinity.

Question 8

The z value associated with a two-sided 95% confidence interval is ___.
A)1.28
B)1.645
C)1.96
D)2.575
E)2.33

Accepted Answer

A two-sided 95% confidence interval corresponds to a level of significance of 0.025 in each tail of the normal distribution. The z score that corresponds to a level of 0.025 in the upper tail is 1.96, and the z score that corresponds to a level of 0.025 in the lower tail is -1.96. Therefore, the z value associated with a two-sided 95% confidence interval is 1.96. The z value associated with a two-sided 95% confidence interval is 1.96. This is a commonly used value in statistics and is also known as the standard normal deviate.

Question 9

In estimating the sample size necessary to estimate a population mean, the error of estimation, E, is equal to the difference between the sample mean and the population mean.

Accepted Answer

The error of estimation, E, is defined as the difference between the sample mean and the population mean, representing the margin of error in estimating the population mean.

Question 10

In order to find values in the t distribution table, you must determine the appropriate degrees of freedom based on the sample sizes.

Accepted Answer

This is true. The degrees of freedom are based on the sample sizes and are essential in finding the appropriate value in the t distribution table. The t distribution table uses degrees of freedom to determine the critical value for a given level of significance and sample size. The degrees of freedom are determined by subtracting 1 from the sample size.

Question 11

An assumption underlying the use of t statistic in sample-based estimation is that the population is normally distributed.

Accepted Answer

The t statistic is based on the assumption that the population is normally distributed. If this assumption is not met, alternative statistical tests may be necessary. The t statistic assumes that the population from which the sample is drawn is normally distributed. This assumption is necessary to ensure that the sampling distribution of the mean is also normally distributed. However, in practice, this assumption may not always hold, and other statistical techniques may need to be used.

Question 12

In determining the interval estimates for a population variance using the sample variance, it is appropriate to use the values from a chi-square distribution rather than a t distribution.

Accepted Answer

The interval estimates for a population variance using the sample variance should use the values from a chi-square distribution. This is because the sample variance follows a chi-square distribution, and the variability in the estimation of the population variance depends on the sample size, which is accounted for by the degrees of freedom in the chi-square distribution. Conversely, a t distribution would be used for interval estimates of a population mean using a sample mean. This is true. The interval estimate for population variance typically involves calculating the confidence interval using the sample variance and the chi-square distribution with degrees of freedom equal to the sample size minus 1. This is because the distribution of sample variance follows a chi-square distribution rather than a t distribution.

Question 13

If the degrees of freedom in a t distribution increase, difference between the t values and the z values will also increase.

Accepted Answer

The difference between t values and z values decreases as the degrees of freedom in a t distribution increase. As the sample size increases, the t distribution becomes more similar to the standard normal distribution (z distribution), resulting in smaller discrepancies between t and z values. As the degrees of freedom increase, the t distribution approaches the standard normal distribution (z distribution), which means the difference between the t values and the z values will decrease.

Question 14

When a range of values is used to estimate a population parameter, it is called a range estimate.

Accepted Answer

When a range of values is used to estimate a population parameter, it is called an interval estimate. When a range of values is used to estimate a population parameter, it is called an interval estimate.

Question 15

If the population is not normal but its standard deviation, σ, is known and the sample size, n is large (n ≥ 30), z-distribution values may be used to determine interval estimates for the population mean.

Accepted Answer

This is correct as the Central Limit Theorem allows us to use the z-distribution to estimate the population mean even if the population is not normal but the sample size is large enough. This statement is true. When the population is not normal but the sample size is large (n ≥ 30) and the standard deviation is known, the Central Limit Theorem allows for z-distribution values to be used in determining interval estimates for the population mean.

Question 16

In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the values from a t distribution rather than the z distribution.

Accepted Answer

In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the values from a normal distribution (z distribution) since the sample size is typically large enough for the central limit theorem to apply. The t distribution is used when the sample size is small or the population standard deviation is unknown.

Question 17

Use of the chi-square statistic to estimate the population variance is extremely robust to the assumption that the population is normally distributed.

Accepted Answer

The chi-square statistic for estimating population variance is sensitive to the assumption of normality in the underlying population. If the population is not normally distributed, the chi-square test may not be appropriate or reliable.

Question 18

Eugene Gates, Marketing Director of Mansfield Motors Manufacturers, Inc.'s Electrical Division, is leading a study to assess the relative importance of product features.An item on a survey questionnaire distributed to 100 of Mansfield's customers asked them to rate the importance of "ease of maintenance" on a scale of 1 to 10 (with 1 meaning "not important" and 10 meaning "highly important").His staff assembled the following statistics:  If Eugene concludes that the average rate of "ease of maintenance" for all customers is 7.5, he is using ___.
A)a range estimate
B)a statistical parameter
C)a point estimate
D)an interval estimate
E)a guesstimate

Accepted Answer

Eugene is using a single value to estimate the average rate of "ease of maintenance" for all customers, which is a point estimate. He is not providing a range or an interval estimate, and he is using a statistical parameter (the sample mean) to make the estimate rather than a guesstimate.

Question 19

If the population is normal and its standard deviation, σ, is unknown and the sample size, n, is large (n ≥ 30), interval estimates for the population mean must be determined using z values.

Accepted Answer

When the population standard deviation is unknown and the sample size is large, the t-distribution is typically used for interval estimates of the population mean, although the z-distribution can be used as an approximation.

Question 20

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package.Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs.If Catherine concludes that 17% of all households prefer the new package, she is using a ___.
A)a point estimate
B)a range estimate
C)a statistical parameter
D)an interval estimate
E)an exact estimate

Accepted Answer

Catherine is using the sample proportion of households (17%) as an estimate for the proportion of all households that prefer the new package. This is a point estimate.

Quiz 8: Statistical Inference: Estimation for Single Populations

The z value associated with a two-sided 90% confidence interval is ___.