Question 1

In determining the level of confidence,any level of confidence is possible,but marketing researchers typically use between 60 percent and 100 percent ,depending on the importance of the issue and how much the client has to spend on the research.

Accepted Answer

Marketing researchers typically use confidence levels of 90%, 95%, or 99%, as these are standard levels that balance precision and practicality. Levels like 60% are not commonly used because they do not provide sufficient reliability.

Question 2

If you calculate sample size with an e of 3 percent,and then you decide to change e to 5 percent,the required sample size will go up.

Accepted Answer

Increasing the margin of error (e) from 3% to 5% will decrease the required sample size, as a larger margin of error allows for more variability in the data.

Question 3

With the 99% level of confidence,the corresponding z value is 2.58.

Accepted Answer

This is true. A 99% level of confidence corresponds to a z value of 2.58 based on the standard normal distribution table.

Question 4

Using the confidence interval formula for calculating sample size,the amount of variability believed to be in the population must be estimated.

Accepted Answer

The calculation of sample size using the confidence interval formula requires an estimation of the population variability or standard deviation. This is necessary to determine the required sample size that will give an accurate and precise estimate of the population mean with a certain level of confidence.

Question 5

The arbitrary approach to sample size determination takes the desired level of accuracy into account.

Accepted Answer

The arbitrary approach to sample size determination does not take the desired level of accuracy into account, but rather relies on the researcher's judgment or convenience.

Question 6

Variability (standard deviation)of a population where a mean is being estimated may be estimated by dividing the range by 6.

Accepted Answer

The range divided by 6 is a rough estimate of the standard deviation for a normal distribution, as the range covers approximately six standard deviations (three on each side of the mean).

Question 7

The basic concept of the central limit theorem is that all research findings are limited in their application simply because they are based upon a sample and not a census.

Accepted Answer

The basic concept of the central limit theorem is that for a large sample size, the distribution of sample means will be normal regardless of the underlying population distribution, and the mean of the sample means will be equal to the population mean. It is not specifically about the limitation of research findings based on a sample.

Question 8

It is almost always up to the researcher to educate the manager on what might be acceptable or "standard" sample error.

Accepted Answer

Sample error is a statistical concept that may not be well understood by all managers. Therefore, it is usually up to the researcher to educate the manager on what level of sample error is acceptable or standard for a particular study.

Question 9

In a "Yes/No" question,50 percent "Yes" and 50 percent "No" shows less variability than does 90 percent "Yes" and 10 percent "No."

Accepted Answer

A 50/50 distribution shows more variability than a 90/10 distribution because there is more uncertainty and less predictability in the outcome.

Question 10

Researchers should follow to the sample size formula closely when calculating sample size.No other consideration,such as the cost to the client,should be considered,as it will surely lower the accuracy of the study.

Accepted Answer

While the sample size formula should be followed to ensure statistical accuracy, other considerations such as cost to the client or practicality may impact the feasibility of the study. Researchers may need to find a balance between statistical accuracy and practicality in determining sample size.

Question 11

In sample size formulae,acceptable sample error is noted by "e."

Accepted Answer

Acceptable sample error is commonly represented by "e" in sample size formulae.

Question 12

Using the confidence interval formula for calculating sample size,the level of confidence desired to the estimate of the population values must be determined and is represented in the formula by the z value.

Accepted Answer

The level of confidence desired is represented by the z value in the confidence interval formula for calculating sample size.

Question 13

The desired accuracy should NOT be considered in order to calculate the proper sample size.This is because accuracy cannot be determined until the data are collected and analyzed.

Accepted Answer

The desired accuracy is a critical factor in determining the proper sample size, as it helps ensure that the sample is representative enough to achieve reliable results.

Question 14

The axiom,"You can take any finding in the survey,replicate the survey with the same probability sample size,and you will be very likely to find the same finding within the ± percent range of the original finding," is based on the idea of the confidence interval.

Accepted Answer

The statement is based on the concept of confidence interval, which is a measure of the uncertainty around a survey finding. The confidence interval indicates the range of values within which the true population parameter is likely to lie with a certain degree of confidence. Replicating the survey with the same probability sample size has the potential to yield similar confidence intervals and hence the same finding within a certain range of the original finding.

Question 15

A probability sample size can be a very tiny percent of the population size and still be very accurate (have little sample error).

Accepted Answer

This statement is true. Probability samples are designed to be representative of the entire population, so even a small sample size can accurately reflect the characteristics of the larger population if they are selected randomly and with proper sampling techniques. The larger the sample size, the more accurate the estimate will be, but even a small sample size can provide reliable results.

Question 16

There is a separate sample size formula for estimating a percentage of the population than for estimating a mean of the population.

Accepted Answer

The sample size formula for estimating a percentage of the population involves the population proportion and the desired level of precision, while the sample size formula for estimating a mean of the population involves the population standard deviation, the desired level of precision, and the level of confidence. Therefore, the formulas are different for these two types of estimates.

Question 17

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

Accepted Answer

When the population is small, the sample size needs to be adjusted to prevent bias and ensure representativeness. However, for larger populations, the sample size determination is not solely based on the population size but also on other factors such as the desired level of precision and confidence.

Question 18

The conventional approach to sample size determination follows some convention or number believed somehow to be the "correct" sample size.

Accepted Answer

The conventional approach to sample size determination involves using statistical calculations and assumptions to determine the appropriate sample size for a given study, rather than relying on a single "correct" number.

Question 19

The most significant factor in calculating sample size (n)is the size of the population (N).For example,if you calculated that you needed a sample size of 300 in order to have an accurate sample for your hometown,it would take at least 10 times this amount,or about 3,000,in order to have an accurate sample representing the entire United States.

Accepted Answer

The most significant factors in calculating sample size are the desired confidence level, margin of error, and population variability, not the size of the population.

Question 20

It is "true" to say that,in practice,you can estimate variability in the population by using one of three methods: (a)set pq to the most conservative amounts of 50 percent/50 percent, (b)estimate pq based upon prior research studies,or (c)conduct a pilot study.

Accepted Answer

This is a commonly used practice in statistics to estimate variability in a population. However, it is important to note that using more accurate estimates of p and q, such as from prior research studies or a pilot study, will result in more precise estimates of variability.

Quiz 10: Determining the Size of a Sample