Question 1

A random sample size can be a very tiny percent of the population size and still have a small margin of sample error.

Accepted Answer

A random sample size with a small margin of error can be achieved by using appropriate sampling techniques, such as probability sampling and stratified sampling, and by ensuring that the sample is representative of the population. A larger sample size usually results in a smaller margin of error, but a tiny sample can still have a small margin of error if it is well-designed and representative.

Question 2

The variability believed to be in the population,the acceptable margin of sample error,and the level of confidence required in your estimates of the population values describe the basic elements of the central limit theorem.

Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. It does not directly involve variability in the population, margin of error, or confidence levels, which are more related to statistical inference and hypothesis testing concepts.

Question 3

Because the sampling process is imperfect,it is inappropriate to use an estimate of sampling error in the calculation of this range.

Accepted Answer

Sampling error estimates are crucial for calculating confidence intervals or margins of error, acknowledging the imperfections in the sampling process and providing a range within which the true population parameter is likely to fall.

Question 4

When applying the standard sample size formula using percentages,there are two alternatives: (1)expect the worst case or(2)guesstimate the actual variability.

Accepted Answer

When applying the standard sample size formula using percentages, it is recommended to expect the worst-case scenario or assume the highest variability to ensure a sufficiently large sample size.

Question 5

Margin of sample error can be calculated with a simple formula and expressed as a ±% number.

Accepted Answer

Margin of sample error is usually expressed as a ±% number and is calculated using a formula that takes into account the sample size, the confidence level, and the variability in the data. Therefore, the statement is true.

Question 6

If respondents are evenly spread across the question's response options,there is much variability because respondents are quite dissimilar.

Accepted Answer

If respondents are evenly spread across the question's response options, it means that there is no clear preference or consensus among the respondents. This suggests that there is much variability, indicating that respondents are dissimilar in their views, opinions, or experiences. Therefore, option A is true.

Question 7

With a sample size of 1,000 or more,there is a significant gain in accuracy especially when doubling or tripling the sample size.

Accepted Answer

Doubling or tripling the sample size from 1,000 does not significantly increase accuracy due to the law of diminishing returns; the gain in precision decreases as sample size increases beyond a certain point.

Question 8

The marketing manager intuitively knows that small samples are less accurate,on average,than are large samples.But it is rare for a marketing manager to think in terms of sample error.

Accepted Answer

The statement accurately reflects the fact that while marketing managers may understand the general principle that larger samples are more reliable, they may not be familiar with the concept of sample error and its implications for measurement accuracy.

Question 9

A 90/10 split in response signifies maximum variability(dissimilarity)in the population,whereas a 50/50 split signifies little variability.

Accepted Answer

A 50/50 split signifies maximum variability or dissimilarity in the population because it indicates an even distribution of two categories, showing that the population is as divided as possible. A 90/10 split suggests less variability, as one category dominates significantly over the other.

Question 10

A researcher can calculate sample size using either a percentage or a mean.

Accepted Answer

A researcher can calculate sample size using either a percentage or a mean. For example, in a survey or study, the researcher may want to estimate the percentage of people who are in favor of a particular policy, or they may want to estimate the average amount of time that people spend on a certain activity. In either case, they can use statistical methods to calculate the sample size needed to achieve a desired level of precision and confidence in the results.

Question 11

The only time the population size is a consideration in sample size determination is in the case of a"small population,"

Accepted Answer

When the population size is small, it affects the sample size determination because a larger percentage of the population is included in the sample, and the sample size needs to be adjusted accordingly to ensure representativeness. However, for larger populations, the population size does not have a significant impact on sample size determination.

Question 12

Any p/q combination other than 50%/50% will result in a higher calculated sample size because p times q is in the numerator of the formula.

Accepted Answer

The product p*q is maximized at 50%/50%, resulting in the largest sample size. Any deviation from this ratio decreases the product, thus reducing the sample size.

Question 13

When researchers find a wide dispersion of responses-that is,when they do not find one response option accounting for a large number of respondents relative to the other items-researchers say that the results have much variability.

Accepted Answer

When researchers find a wide dispersion of responses or a large range of responses without one option being significantly more common than the others, the results are considered to have high variability.

Question 14

If the project director has conflicting information or is worried about the timeliness or some other aspect of the information about the population's variability,he or she may begin the full study early so he or she can estimate p more confidently.

Accepted Answer

Starting the full study early due to conflicting information or concerns about timeliness is not a standard approach to estimate population variability more confidently. Instead, preliminary studies or pilot tests are typically conducted to resolve such issues before the full study.

Question 15

If most respondents indicate the same answer on the response scale,the distribution has much variability because respondents are highly similar.

Accepted Answer

If most respondents indicate the same answer on the response scale, the distribution has low variability because there is little difference between the responses. High similarity would lead to a narrow distribution with low variability.

Question 16

In almost all situations,the sample size and the size of the population are related to each other.

Accepted Answer

The sample size needed for a study does not necessarily increase with the size of the population. Beyond a certain point, larger populations do not require proportionally larger samples for statistically significant results.

Question 17

A lower sample size means less effort,time,and cost,so there are good reasons for a researcher to try to estimate p rather than to take the worst case.

Accepted Answer

A lower sample size means less effort, time, and cost, making it a practical choice for researchers. Therefore, it is more efficient to estimate p rather than taking the worst-case scenario, which would usually require a larger sample size and more resources.

Question 18

The amount of sample error the researcher will permit to be associated with the survey is relational margin of sample error.

Accepted Answer

The term "relational margin of sample error" is incorrect; the correct term is "margin of error" or "margin of sampling error," which refers to the amount of error that can be tolerated in the results of a survey or poll, indicating the confidence in the accuracy of the results.

Question 19

A confidence interval is based on the normal,or bell-shaped,curve commonly found in statistics.

Accepted Answer

A confidence interval is based on the assumption that the data follows a normal distribution, which is a bell-shaped curve.

Question 20

You can take any finding in the survey,replicate the survey with a random sample of the same size,and be"very likely"to find the same finding within the ±% range of the original sample's finding.

Accepted Answer

This statement is true. The margin of error in a survey is calculated based on the sample size and the level of confidence. With a larger sample size, the margin of error decreases, but even with a small sample size, if the survey is well-designed and conducted, the findings are likely to be replicated with a similar margin of error. Therefore, if a finding in a survey is replicated with a random sample of the same size, it is very likely to fall within the same range of ±%, which is the margin of error of the survey.

Quiz 10: Determining the Size of a Sample