Question 1

The confidence level is the probability that a confidence interval will include the population parameter.

Accepted Answer

The confidence level represents the probability that a confidence interval, constructed from sample data, will contain the true population parameter.

Question 2

The concept of a sampling distribution enables us to use probability theory to make inferences about the population values.

Accepted Answer

The concept of a sampling distribution allows us to use probability theory to make inferences about population values.

Question 3

When determining the sample size, if the population standard deviation, s, is unknown and an estimate is used, the standard deviation should be re-estimated once the sample has been drawn.Next a revised confidence interval should be calculated to determine the precision level actually obtained.

Accepted Answer

When the population standard deviation is unknown, it is common to use the sample standard deviation as an estimate. However, once the sample is drawn and the standard deviation is estimated from the sample, it is important to revise the confidence interval and recalculate the precision level based on the updated estimate. This ensures that the sample size and results are accurate and reliable.

Question 4

The statistical approach to determining sample size is based on the construction of confidence intervals around sample means or proportions.

Accepted Answer

The statistical approach to determining sample size involves calculating the necessary sample size based on the desired confidence level, margin of error, and variability of the population. Confidence intervals are then constructed around sample means or proportions as a way to estimate the true population parameter with a certain level of accuracy.

Question 5

The process of generalizing the sample results to the population results is called statistical inference.

Accepted Answer

This statement is true. Statistical inference involves using sample data to make conclusions or predictions about a larger population.

Question 6

Specify the level of confidence is the first step in the confidence interval approach to determining sample size.

Accepted Answer

The answer of Specify the level of confidence is the...

Question 7

Assuming no measurement error, the reliability of an estimate of a population parameter can be assessed in terms of its standard error.

Accepted Answer

Standard error is a measure of the precision of an estimate and is used to assess the reliability of the estimate.

Question 8

The confidence interval approach to sample size determination is based on the construction of confidence intervals around the means or proportions using the standardized variate formula.

Accepted Answer

The answer of The confidence interval approach to sample size...

Question 9

The sampling distribution is the probability of the values of a sampling statistic computed for each possible sample that could be drawn from the target population under a specified sampling plan.

Accepted Answer

The answer of The sampling distribution is the probability of...

Question 10

If the researcher is required to estimate several parameters, not just one, the calculation of sample size in these cases should be based on a consideration of all the parameters that must be estimated.

Accepted Answer

When estimating multiple parameters, the sample size calculation should take into account all of the parameters that need to be estimated, as each parameter may require a different sample size for accurate estimation.

Question 11

In the statistical approach to determining sample size, the precision level is specified in the end.

Accepted Answer

In the statistical approach to determining sample size, the precision level (also known as the margin of error) is specified at the beginning of the study design process, not at the end. This helps in determining the required sample size to achieve the desired precision for the study's estimates.

Question 12

Survey System (www.surveysystem.com)and the Discovery Research Group (www.drgutah.com)are Web sites on the Internet that offer free use of sample size and/or confidence interval calculators.

Accepted Answer

Both websites offer free use of sample size and/or confidence interval calculators.

Question 13

When using the confidence interval approach to sample size determination, in some cases, precision is specified in relative rather than absolute terms. In other words, it may be specified that the estimate be within plus or minus R percentage points of the mean.

Accepted Answer

This statement is true. Precision can be specified in relative terms, such as being within a certain percentage of the mean. This is often seen in market research studies or surveys where the margin of error is expressed as a percentage.

Question 14

When the sample size is 10 percent or more of the population size, the standard error formulas will overestimate the standard deviation of the population mean or proportion. Hence, these should be adjusted by a finite population correction factor.

Accepted Answer

This is true as when the sample size is a significant fraction of the population size, it can affect the accuracy of the standard error formula. Therefore, applying the finite population correction factor helps to adjust the standard error formula and provide a more accurate estimate of the population mean or proportion.

Question 15

Two major nonresponse issues in sampling are improving response rates and adjusting for nonresponse.

Accepted Answer

Both improving response rates and adjusting for nonresponse are common nonresponse issues in sampling. Improving response rates involves finding ways to encourage participants to respond to surveys and studies, while adjusting for nonresponse involves accounting for the potential bias introduced by those who do not respond.

Question 16

The z value for a point is the number of standard deviations a point is away from the mean.

Accepted Answer

The answer of The z value for a point is...

Question 17

The sampling distribution of the mean is a binomial distribution.

Accepted Answer

The sampling distribution of the mean is actually a normal distribution, as long as the sample size is sufficiently large and the population standard deviation is known or the sample size is large enough to approximate it. The binomial distribution applies to a different type of probability distribution involving success and failure outcomes.

Question 18

When using the confidence interval approach to sample size determination, if the statistic of interest is a proportion, rather than a mean, the approach to sample size determination is very different.

Accepted Answer

The approach to sample size determination for a proportion involves a similar conceptual framework as for a mean, using a formula that accounts for the desired confidence level, the variability in the population (estimated by the proportion in the case of categorical data), and the margin of error. The formulas differ in their specifics (e.g., using the standard deviation for means vs. the standard error for proportions) but the underlying principles of determining how large a sample is needed to estimate the parameter of interest with a certain level of confidence and precision are consistent across both types of statistics.

Question 19

The statistically determined sample size is the net or final sample size-the sample remaining after eliminating potential respondents who do not qualify or who do not complete the interview.

Accepted Answer

The statistically determined sample size refers to the initial sample size needed to ensure sufficient statistical power in the study. The net or final sample size is the sample size that remains after eliminating potential respondents who do not qualify or who do not complete the interview. Therefore, the statement is true.

Question 20

The confidence level is the range into which the true population parameter will fall, assuming a given level of confidence.

Accepted Answer

The confidence level represents the probability that the confidence interval contains the true population parameter, not the range itself. The confidence interval is the actual range estimate.

Quiz 12: Sampling: Final and Initial Sample Size Determination