Question 1

The value for for a 95% confidence interval when is 26.119.

Accepted Answer

The value for a 95% confidence interval when z is 26.119 is 0.995.

Question 2

When computing a confidence interval for a population mean using raw data, round off to two more
decimal places than the number of decimal places in the original data.

Accepted Answer

False

Question 3

The value for for a 99% confidence interval when is 9.262.

Accepted Answer

A 99% confidence interval has a larger range than a 95% or 90% confidence interval, so it would be expected to have a larger value for the interval. Therefore, a value of 9.262 for a 99% confidence interval is plausible.

Question 4

A confidence interval was constructed around a proportion. The interval was from 13.5% to 21.5%. The
proportion that was used to construct this interval was 17.5%.

Accepted Answer

The proportion used to construct the interval (17.5%) falls within the interval itself (from 13.5% to 21.5%), so it is true.

Question 5

The rounding rule for a confidence interval for a proportion is to round off to three decimal places.

Accepted Answer

This is true. Confidence intervals for proportions are commonly rounded to three decimal places.

Question 6

Only the degree of confidence and the maximum error are necessary to determine the sample size if one
uses the "conservative" value for the standard error.

Accepted Answer

The conservative approach assumes the maximum variability (p=0.5) for the standard error, allowing the sample size to be determined using only the degree of confidence and maximum error.

Question 7

The width of a confidence interval for a population mean that is based on the t-distribution varies from
sample to sample even if the sample size and confidence level is kept fixed.

Accepted Answer

The width of a confidence interval depends on the standard error of the mean which varies from sample to sample. As the t-distribution takes into account the sample size, the degree of variability also changes from sample to sample, resulting in different confidence interval widths.

Question 8

According to Statistics Canada, on July 1, 2006 the population size of the province of Quebec was
7,651,531 whereas Nova Scotia was considerably smaller at 934,405. Thus the margin of error for a
Gallup Poll based on a random sample of 1000 Nova Scotians is smaller than that based on a random
sample of 1000 Quebeckers.

Accepted Answer

The margin of error in a poll is determined by the sample size and not the population size. Since both samples are of the same size (1000), the margin of error would be the same for both provinces.

Question 9

A retailer wants to estimate with 99% confidence the number of people who buy at his store. A previous
study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3%
of the

Accepted Answer

The answer of A retailer wants to estimate with 99%...

Question 10

A chi-square distribution is negatively skewed.

Accepted Answer

The answer of A chi-square distribution is negatively skewed....

Question 11

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or
approximately normally distributed.

Accepted Answer

This statement is incorrect. The t-distribution should be used when the sample size is small (less than 30) or when the population standard deviation is unknown. When the sample size is greater than 30 and the variable is normally or approximately normally distributed, the standard normal distribution can be used instead.

Question 12

The confidence level of an interval estimate of a parameter is the probability that the interval estimator
will contain the parameter.

Accepted Answer

This is the definition of confidence level in interval estimation.

Question 13

A chi-square variable cannot be negative, and the distributions are positively skewed.

Accepted Answer

A chi-square variable cannot be negative as it is always the sum of the squared deviations from the expected values, which are always non-negative. The distributions of chi-square variables are also positively skewed, meaning that there are more scores in the lower range of the distribution and a few high scores that skew the distribution to the right.

Question 14

Noting that the critical z-value for a 95% confidence interval for a proportion is almost equal to 2, it
can be seen that the required sample size is approximately equal to the reciprocal of the squared desired
margin of error.

Accepted Answer

The statement is true. The critical z-value for a 95% confidence interval is 1.96, which is nearly equal to 2. The formula for calculating the sample size for a proportion is n = (z^2 * p * q) / E^2 where z is the critical value, p is the estimated proportion, q is 1-p, and E is the desired margin of error. Rearranging this formula, we get E^2 = (z^2 * p * q) / n. Since z is approximately equal to 2, the reciprocal of the squared desired margin of error is approximately equal to the sample size needed, which supports the statement.

Question 15

$$\text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. }$$

Accepted Answer

The answer of \[\text { The value of } \alpha...

Question 16

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records
for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation
of 3.9 minutes. Jennifer's maximum error of estimate would be 1.4 minutes.

Accepted Answer

To find the confidence interval, we can use the formula:

CI = x̄ ± z*(σ/√n)

where x̄ is the sample mean (20.5), σ is the sample standard deviation (3.9), n is the sample size (30), and z is the critical value from the standard normal distribution for a 95% confidence level (which is approximately 1.96).

Plugging in the values, we get:

CI = 20.5 ± 1.96*(3.9/√30)
   = 20.5 ± 1.39

This means that we are 95% confident that Jennifer's true commute time falls within the range of 19.11 to 21.89 minutes. Since the maximum error of estimate given is 1.4 minutes, and the actual range of the confidence interval is within 1.39 minutes, the statement is true.

Question 17

The width of a confidence interval for a population variance is of constant width for fixed values of the
sample size and confidence level.

Accepted Answer

The width of a confidence interval for a population variance depends on the sample size and the confidence level. As the sample size increases, the width of the interval decreases. As the confidence level increases, the width of the interval increases. Therefore, the width of a confidence interval for a population variance is not of constant width for fixed values of the sample size and confidence level.

Question 18

An interval estimate may or may not contain the value of the parameter being estimated.

Accepted Answer

An interval estimate provides a range of likely values for the parameter being estimated. It is possible that the true value of the parameter falls within the range, but it is also possible that it falls outside of the range. Therefore, an interval estimate may or may not contain the value of the parameter being estimated.

Question 19

The (estimated) standard error of the mean is larger than the standard deviation of the sample from which
it was derived.

Accepted Answer

The standard error of the mean is the standard deviation divided by the square root of the sample size, making it smaller than the standard deviation.

Question 20

The t-distribution has a variance that is greater than one.

Accepted Answer

The variance of the t-distribution is equal to its degrees of freedom divided by its degrees of freedom minus 2, and this value is greater than 1 for all t-distributions with fewer than 3 degrees of freedom. For t-distributions with more than 2 degrees of freedom, the variance approaches 1 as the degrees of freedom increase.

Quiz 6: Confidence Intervals and Sample Size

The value for for a 95% confidence interval when is 26.119.

When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.

The value for for a 99% confidence interval when is 9.262.

A confidence interval was constructed around a proportion. The interval was from 13.5% to 21.5%. The proportion that was used to construct this interval was 17.5%.

The rounding rule for a confidence interval for a proportion is to round off to three decimal places.

Only the degree of confidence and the maximum error are necessary to determine the sample size if one uses the "conservative" value for the standard error.

The width of a confidence interval for a population mean that is based on the t-distribution varies from sample to sample even if the sample size and confidence level is kept fixed.

A retailer wants to estimate with 99% confidence the number of people who buy at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the

A chi-square distribution is negatively skewed.

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

The confidence level of an interval estimate of a parameter is the probability that the interval estimator will contain the parameter.

A chi-square variable cannot be negative, and the distributions are positively skewed.

Noting that the critical z-value for a 95% confidence interval for a proportion is almost equal to 2, it can be seen that the required sample size is approximately equal to the reciprocal of the squared desired margin of error.

$\text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. }$ $\text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. }$

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation of 3.9 minutes. Jennifer's maximum error of estimate would be 1.4 minutes.

The width of a confidence interval for a population variance is of constant width for fixed values of the sample size and confidence level.

An interval estimate may or may not contain the value of the parameter being estimated.

The (estimated) standard error of the mean is larger than the standard deviation of the sample from which it was derived.

The t-distribution has a variance that is greater than one.

Quiz 6: Confidence Intervals and Sample Size

The value for for a 95% confidence interval when is 26.119.

When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.

The value for for a 99% confidence interval when is 9.262.

A confidence interval was constructed around a proportion. The interval was from 13.5% to 21.5%. The proportion that was used to construct this interval was 17.5%.

The rounding rule for a confidence interval for a proportion is to round off to three decimal places.

Only the degree of confidence and the maximum error are necessary to determine the sample size if one uses the "conservative" value for the standard error.

The width of a confidence interval for a population mean that is based on the t-distribution varies from sample to sample even if the sample size and confidence level is kept fixed.

A retailer wants to estimate with 99% confidence the number of people who buy at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the

A chi-square distribution is negatively skewed.

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

The confidence level of an interval estimate of a parameter is the probability that the interval estimator will contain the parameter.

A chi-square variable cannot be negative, and the distributions are positively skewed.

Noting that the critical z-value for a 95% confidence interval for a proportion is almost equal to 2, it can be seen that the required sample size is approximately equal to the reciprocal of the squared desired margin of error.

The value of α/2 used in the figure below is 0.025. \text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. } The value of α/2 used in the figure below is 0.025.

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation of 3.9 minutes. Jennifer's maximum error of estimate would be 1.4 minutes.

The width of a confidence interval for a population variance is of constant width for fixed values of the sample size and confidence level.

An interval estimate may or may not contain the value of the parameter being estimated.

The (estimated) standard error of the mean is larger than the standard deviation of the sample from which it was derived.

The t-distribution has a variance that is greater than one.

$\text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. }$ $\text { The value of } \alpha / 2 \text { used in the figure below is } 0.025 \text {. }$