Question 1

The population variance is a measure of the population dispersion, based on the degree to which a response differs from the population mean response.

Accepted Answer

The definition of population variance is correct. It measures the spread of data around the population mean response.

Question 2

Two samples are drawn from the same population with a known variance, ².If the sample sizes are 100 and 400, then the standard error of the mean of the former sample will be half that of the latter.

Accepted Answer

The standard error of the mean is inversely proportional to the square root of the sample size. So, if the sample size is 4 times larger, the standard error of the mean will be half as large.

Question 3

The sample mean is not known, but it can be estimated from the population characteristics.

Accepted Answer

The sample mean is calculated from the sample data itself, not estimated from the population characteristics.

Question 4

Bo Derek calculates that she needs a sample size of 200, given the estimated mean, accuracy variance and required Z-score.However, she learns that the variance is actually one-half of what she originally believed.Her required sample size will now be 
a) 100 
b) 800 
c) 400 
d) 50 
e) none of the above

Accepted Answer

The answer of Bo Derek calculates that she needs a...

Question 5

If the population variance is 4, the sample standard deviation must be 2.

Accepted Answer

The formula for the relationship between population variance and sample standard deviation is: variance = (n-1)/n * sample standard deviation^2. Therefore, if the population variance is known to be 4, we cannot determine the sample standard deviation without additional information about the sample size (n).

Question 6

If we wanted to be 95 percent confident that we wouldn't make an error of more than 1 unit in our estimate of  for = 2), we would need a sample size of approximately 16.

Accepted Answer

The formula for calculating the margin of error is 1.96 * standard deviation / square root of sample size. Since we want the margin of error to be less than or equal to 1, we can set up the inequality 1.96 * standard deviation / square root of sample size ≤ 1. Solving for the sample size, we get approximately 15.6, which rounds up to 16. Therefore, we would need a sample size of approximately 16 to be 95% confident that we wouldn't make an error of more than 1 unit in our estimate of F1F1F1S1F1F1F10 for F1F1F1S1F1F1F10 = 2.

Question 7

As the sample size becomes larger, the mean of the sampling distribution becomes 
a) greater than the population mean 
b) smaller than the population mean 
c) equal to the population mean 
d) double that of the population mean

Accepted Answer

The answer of As the sample size becomes larger, the...

Question 8

The sample variance, S², can be used to estimate the population variation.

Accepted Answer

The sample variance is used to estimate the population variance.

Question 9

A 95 percent confidence interval will be smaller than a 90 percent confidence interval.

Accepted Answer

A 95 percent confidence interval is wider than a 90 percent confidence interval because it requires capturing more of the data to be 95% confident, thus extending the range of values.

Question 10

If the allowed error is increased, the required sample size would decrease.

Accepted Answer

When the allowed error is increased, the required sample size decreases because a larger margin of error means that the researcher can be less precise in their measurements, which in turn requires a smaller sample size.

Question 11

It does not make sense to use disproportionate sampling if one of the subgroups of the population is a relatively small percentage of the population

Accepted Answer

Disproportionate sampling is often used precisely because a subgroup of the population is a small percentage of the overall population, and the research aims to ensure adequate representation of that subgroup in the sample for more detailed analysis.

Question 12

If two random samples of equal size are drawn from the same population, we should expect the mean of both samples to be identical.

Accepted Answer

While the means of the two samples may be close, it is highly unlikely that they will be identical due to random sampling variation.

Question 13

The standard error of the mean is the same as the 
a) standard deviation of the population 
b) standard deviation of the normal distribution 
c) standard deviation of the sampling distribution 
d) none of the above

Accepted Answer

The answer of The standard error of the mean is...

Question 14

The distribution which we say always assume to be "normal" or bell shaped is the 
a) sampling distribution 
b) population distribution 
c) sample distribution
d) variance distribution 
e) standard distribution

Accepted Answer

The answer of The distribution which we say always assume...

Question 15

When a complex multi-stage design is involved, a common approach is to replicate the entire sampling plan and get various independent estimates of the sample mean.

Accepted Answer

Replicating the entire sampling plan helps to get various independent estimates of the sample mean, making it a common approach in complex multi-stage designs.

Question 16

The two population characteristics of most interest to researchers are  and The two population characteristics of most interest to researchers.

Accepted Answer

These are indeed two population characteristics of interest to researchers. F1F1F1S1F1F1F10 refers to the genetic makeup of individuals, while F1F1F1S1F1F1F10 refers to their physical traits. Both characteristics are important in understanding genetic inheritance and the relationship between genotype and phenotype.

Question 17

A researcher takes a modest sample and, if results are worthwhile, opts for a larger sample.This type of sampling is called sequential sampling.

Accepted Answer

Sequential sampling involves starting with a smaller sample size and then deciding whether to continue sampling based on the results obtained. If the results are worthwhile, then the researcher will continue sampling with a larger sample.

Question 18

If all members of the population have identical opinions on an issue, a sample of one is unsatisfactory.

Accepted Answer

If all members of the population have identical opinions on an issue, a sample of one would be representative of the entire population's opinion on that issue.

Question 19

Which of the following factors does the interval estimate depends on? sample size?
a) sample size 
b) confidence level 
c) population standard deviation 
d) all of the above

Accepted Answer

The answer of Which of the following factors does the...

Question 20

The size of a sample can be determined only by using statistical techniques.

Accepted Answer

The size of a sample can also be determined based on practical considerations such as available time, resources, and feasibility. However, statistical techniques can help in determining the appropriate sample size based on the research question, population size, and variability.

Quiz 15: Sample Size and Statistical Theory

The population variance is a measure of the population dispersion, based on the degree to which a response differs from the population mean response.

Two samples are drawn from the same population with a known variance, 2.If the sample sizes are 100 and 400, then the standard error of the mean of the former sample will be half that of the latter.

The sample mean is not known, but it can be estimated from the population characteristics.

Bo Derek calculates that she needs a sample size of 200, given the estimated mean, accuracy variance and required Z-score.However, she learns that the variance is actually one-half of what she originally believed.Her required sample size will now be a) 100 b) 800 c) 400 d) 50 e) none of the above

If the population variance is 4, the sample standard deviation must be 2.

If we wanted to be 95 percent confident that we wouldn't make an error of more than 1 unit in our estimate of for = 2), we would need a sample size of approximately 16.

As the sample size becomes larger, the mean of the sampling distribution becomes a) greater than the population mean b) smaller than the population mean c) equal to the population mean d) double that of the population mean

The sample variance, S2, can be used to estimate the population variation.