Question 1

If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

Accepted Answer

larger
bigger
greater
more

Question 2

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

Accepted Answer

The correct sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 64, not 17. The formula for calculating the sample size needed in this scenario is:

n = [z*(σ/√n)]^2

Where:
z = the z-score for the desired confidence level (in this case, 1.645 for 90% confidence)
σ = the population standard deviation (10)
n = the sample size needed

Plugging in the values:

n = [1.645*(10/√n)]^2

Solving for n:

n = 64.4

Therefore, the sample size needed is 64, not 17.

Question 3

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is
A)62
B)61
C)8
D)None of these choices.

Accepted Answer

A

Question 4

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was
A)90%
B)95%
C)99%
D)None of these choices.

Accepted Answer

We can use the formula for the margin of error to solve for the confidence level:

Margin of error = z*(sigma/sqrt(n))

We know that the margin of error is 50 and that sigma (population standard deviation) is 250. We also know that the sample size is 97.

50 = z*(250/sqrt(97))

Solving for z, we get:

z = 1.96

This corresponds to a 95% confidence level (using a standard normal distribution table). Therefore, the answer is (B) 95%.

Question 5

The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

Accepted Answer

The answer of The sampling error for a confidence interval...

Question 6

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.

Accepted Answer

n decreases as the confidence level decreases because a lower confidence level means we accept a higher level of uncertainty, thus requiring a smaller sample size to estimate the population mean.

Question 7

The sample size needed to estimate the population mean was found to be 865. If the value of the population standard deviation was 75, and the maximum allowable error was 5, then the confidence level used was 95%.

Accepted Answer

Given, 
Sample size (n) = 865
Standard deviation (σ) = 75
Maximum allowable error = 5 
Confidence level = 95%

Using the formula for calculating the sample size for estimating the population mean, we have:

n = (Z^2 * σ^2) / E^2

Where 
Z = Z-value for the desired confidence level
E = maximum allowable error

Here, 
n = 865
σ = 75
E = 5
For 95% confidence level, Z = 1.96

Substituting the values, we have:

865 = (1.96^2 * 75^2) / 5^2

Solving for Z, we get:

Z = 1.96

Therefore, the answer is True, the confidence level used was 95%.

Question 8

Which of the following statements is false regarding the sample size needed to estimate a population mean? A)It is directly proportional to the population variance. B)It is directly proportional to the square of z _{$\alpha$ / 2}. C)It is directly proportional to the square of the maximum allowable error B. D)None of these choices.

Accepted Answer

The sample size is inversely proportional to the square of the maximum allowable error B, not directly proportional.

Question 9

If the bound on the error of estimation decreases, the sample size ____________________.

Accepted Answer

The answer of If the bound on the error of...

Question 10

When determining the required sample size for a confidence interval, you need to know the population ____________________, the confidence ____________________, and the ____________________ on the error of estimation.

Accepted Answer

The answer of When determining the required sample size for...

Question 11

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

Accepted Answer

When the population standard deviation is higher, it means there is more variability within the population, and therefore more variability within the sample. This requires a larger sample size in order to obtain a representative sample and produce a more accurate estimate of the population mean.

Question 12

If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

Accepted Answer

The answer of If the population standard deviation is guesstimated,...

Question 13

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:
A)166
B)167
C)13
D)None of these choices.

Accepted Answer

The formula for calculating the sample size needed to estimate the population mean with a given error bound and confidence level is:

n = (Zα/2 * σ / E)^2

Where:
Zα/2 = the z-score corresponding to the given confidence level (99%) = 2.58
σ = the population standard deviation = 6
E = the desired error bound = 1.2

Plugging in these values, we get:

n = (2.58 * 6 / 1.2)^2 = 166.6

Since we cannot have a fractional sample size, we round up to the nearest whole number, which gives us:

n = 167

Therefore, the best choice is B) 167.

Question 14

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

Accepted Answer

According to the formula for calculating sample size for estimating population mean with a specified margin of error and confidence level, n = [z*(σ/E)]^2, where z is the z-score corresponding to the specified confidence level, σ is the population standard deviation, and E is the maximum allowable sampling error. If we plug in the given values, we get:

n = [1.96*(4/1)]^2 = 61.55

Since the sample size must be a whole number, we round up to get n = 62. Therefore, the statement is true.

Question 15

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:
A)99%
B)95%
C)90%
D)None of these choices.

Accepted Answer

The answer of The sample size needed to estimate a...

Question 16

The error of estimation is the ____________________ between an estimator and the parameter.

Accepted Answer

The answer of The error of estimation is the ____________________...

Question 17

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

Accepted Answer

The answer of Because n is an integer and we...

Question 18

When determining the sample size necessary for estimating the true population mean, which factor is not of our concern when sampling with replacement?
A)The allowable or tolerable sampling error.
B)The level of confidence desired in the estimate.
C)The population standard deviation.
D)The population size.

Accepted Answer

When sampling with replacement, we assume that the population is infinitely large, making the population size irrelevant for determining the sample size. However, factors such as the allowable sampling error, level of confidence, and population standard deviation are still important considerations when determining sample size.

Question 19

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

Accepted Answer

The answer of Statisticians can control the ____________________ of a...

Question 20

In determining the sample size n needed to estimate the population mean, n decreases as the desired width of the confidence interval decreases.

Accepted Answer

In determining the sample size needed to estimate the population mean, n increases as the desired width of the confidence interval decreases, because a narrower interval requires a larger sample size to achieve the same level of confidence.

Quiz 10: Introduction to Estimation

If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was

The sampling error for a confidence interval is also defined as the of .

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.

The sample size needed to estimate the population mean was found to be 865. If the value of the population standard deviation was 75, and the maximum allowable error was 5, then the confidence level used was 95%.

Which of the following statements is false regarding the sample size needed to estimate a population mean?

If the bound on the error of estimation decreases, the sample size ____________________.

When determining the required sample size for a confidence interval, you need to know the population , the confidence , and the on the error of estimation.

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:

The error of estimation is the ____________________ between an estimator and the parameter.

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

When determining the sample size necessary for estimating the true population mean, which factor is not of our concern when sampling with replacement?

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

In determining the sample size n needed to estimate the population mean, n decreases as the desired width of the confidence interval decreases.

Quiz 10: Introduction to Estimation

If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was

The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.

The sample size needed to estimate the population mean was found to be 865. If the value of the population standard deviation was 75, and the maximum allowable error was 5, then the confidence level used was 95%.

Which of the following statements is false regarding the sample size needed to estimate a population mean?

If the bound on the error of estimation decreases, the sample size ____________________.

When determining the required sample size for a confidence interval, you need to know the population ____________________, the confidence ____________________, and the ____________________ on the error of estimation.

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation σ\sigmaσ is higher.

If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:

The error of estimation is the ____________________ between an estimator and the parameter.

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

When determining the sample size necessary for estimating the true population mean, which factor is not of our concern when sampling with replacement?

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

In determining the sample size n needed to estimate the population mean, n decreases as the desired width of the confidence interval decreases.

The sampling error for a confidence interval is also defined as the of .

When determining the required sample size for a confidence interval, you need to know the population , the confidence , and the on the error of estimation.

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.