Question 1

If we want to find the required sample size for the interval estimation of the population proportion, and no reasonable estimate of this proportion is available, we assume the worst-case scenario under which  = 0.5.

Accepted Answer

This is true. When no reasonable estimate of the population proportion is available, it is common practice to assume a worst-case scenario, which is usually p = 0.5. This assumption provides the largest possible sample size for a given margin of error.

Question 2

Excel does not have a special function that allows to calculate t values.

Accepted Answer

Excel has several functions, such as T.DIST, T.DIST.2T, T.DIST.RT, T.INV, and T.INV.2T, which allow users to calculate t-values and work with t-distributions for statistical analysis.

Question 3

A confidence interval is generally associated with a(n) ________.

Accepted Answer

margin of error

Question 4

For a given confidence level 100(1 - α)% and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.

Accepted Answer

This is because the standard error of the mean, which is the measure of the variability of the sample means around the true population mean, is inversely proportional to the square root of the sample size. As the sample size decreases, the standard error of the mean increases, causing the confidence interval to be wider to accommodate a larger range of values for the population mean.

Question 5

The ________ determine the extent of the broadness of the tails of the distribution.

Accepted Answer

The answer of The ________ determine the extent of the...

Question 6

The width of the confidence interval is ________ times the margin of error.

Accepted Answer

The answer of The width of the confidence interval is...

Question 7

To construct a 95% confidence interval for µ, the sampling distribution of  must be ________.

Accepted Answer

The answer of To construct a 95% confidence interval for...

Question 8

If a random sample of size n is taken from a normal population with a finite variance, then the statistic T = follows the t_df distribution with (n − 1) degrees of freedom, df.

Accepted Answer

This is the definition of the t-distribution.

Question 9

For a given confidence level 100(1 - α)% and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

Accepted Answer

The width of the confidence interval for the population mean is wider, not narrower, as the population standard deviation σ increases, given that the confidence level and sample size remain constant.

Question 10

The t distribution table lists t_df values for selected lower-tail probabilities and degrees of freedom df.

Accepted Answer

The t distribution table typically lists t_df values for selected upper-tail probabilities and degrees of freedom df, not lower-tail probabilities.

Question 11

The sampling distribution of  is based on a normal distribution on samples of any size.

Accepted Answer

The answer of The sampling distribution of  is based...

Question 12

The t_df distribution has broader tails than the z distribution.

Accepted Answer

The t-distribution has broader tails than the standard normal distribution (represented by the z-distribution), meaning it has more probability mass in the tails and a lower peak at the center.

Question 13

The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of z_α_/2 based on the confidence level 100(1 − α)% and the desired margin of error D.

Accepted Answer

The answer of The required sample size for the interval...

Question 14

Like the z distribution, the t_df distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

Accepted Answer

The t-distribution is symmetric and bell-shaped like the z-distribution, but its tails do not cross the horizontal axis; instead, they approach it asymptotically.

Question 15

The t_dfdistribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the t_df distribution is similar to the z distribution.

Accepted Answer

The t-distribution is indeed a family of distributions where the shape depends on the degrees of freedom (df), but for lower values of df, the t-distribution is more spread out with heavier tails compared to the z-distribution. It becomes similar to the z-distribution as the df increases.

Question 16

The confidence coefficient is equal to ________.

Accepted Answer

The answer of The confidence coefficient is equal to ________.
...

Question 17

If a small segment of the population is sampled then an estimate will be less precise.

Accepted Answer

When a smaller sample is taken, there is a higher chance of sampling error, which can result in a less precise estimate.

Question 18

The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

Accepted Answer

This statement is true. The sampling distribution of the underlying statistic is used to calculate the standard error, which is in turn used to develop the confidence interval.

Question 19

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1 - α)%.

Accepted Answer

The width of the confidence interval for the population mean becomes narrower as the confidence level decreases (i.e., as α increases), because a lower confidence level means we are requiring less certainty about where the true population parameter lies, resulting in a narrower interval.

Question 20

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

Accepted Answer

A confidence interval provides a range of values, not a single value, that, with a certain level of confidence, is believed to contain the population parameter of interest.

Quiz 8: Interval Estimation

If we want to find the required sample size for the interval estimation of the population proportion, and no reasonable estimate of this proportion is available, we assume the worst-case scenario under which = 0.5.

Excel does not have a special function that allows to calculate t values.

A confidence interval is generally associated with a(n) ________.

For a given confidence level 100(1 - α)% and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.

The ________ determine the extent of the broadness of the tails of the distribution.

The width of the confidence interval is ________ times the margin of error.

To construct a 95% confidence interval for µ, the sampling distribution of must be ________.

If a random sample of size n is taken from a normal population with a finite variance, then the statistic T = follows the tdf distribution with (n − 1) degrees of freedom, df.

For a given confidence level 100(1 - α)% and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

The t distribution table lists tdf values for selected lower-tail probabilities and degrees of freedom df.

The sampling distribution of is based on a normal distribution on samples of any size.

The tdf distribution has broader tails than the z distribution.

The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of zα/2 based on the confidence level 100(1 − α)% and the desired margin of error D.

Like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution.