Question 1

The exact spread of the t distribution depends on the _________.
A) standard deviation of the sample
B) sample size n
C) number of degrees of freedom
D) z distribution

Accepted Answer

The spread of the t distribution depends solely on the number of degrees of freedom. The formula for the t distribution involves the sample size, n, in the calculation for degrees of freedom, but it is not the direct determinant of the spread. The standard deviation of the sample and the z distribution are not relevant in determining the spread of the t distribution.

Question 2

As standard deviation increases,sample size _____________ to achieve a specified level of confidence.
A) increases
B) decreases
C) remains the same

Accepted Answer

As standard deviation increases, the variability within the sample also increases. This means that in order to achieve a specified level of confidence, a larger sample size will be needed to capture the increased variability and ensure that the results are representative of the population.

Question 3

When constructing a confidence interval for a population mean,if a population is normally distributed and a small sample is taken,then the distribution of is based on the ____________ distribution.
A) z
B) t
C) neither the z nor the t distribution
D) both the z and the t distribution

Accepted Answer

If the population is normally distributed but the sample size is small (n < 30), the distribution of the sample mean is no longer normal and instead follows a t-distribution. Therefore, a t-distribution should be used to construct the confidence interval for the population mean.

Question 4

When the population is normally distributed,population standard deviation σ is unknown,and the sample size is n = 15,the confidence interval for the population mean μ is based on
A) the z (normal)distribution.
B) the t distribution.
C) the binomial distribution.
D) the Poisson distribution.
E) None of the other choices is correct.

Accepted Answer

When the population standard deviation is unknown and the sample size is small (in this case n = 15), the confidence interval for the population mean is based on the t distribution.

Question 5

When the sample size and the sample proportion remain the same,a 90 percent confidence interval for a population proportion p will be ______________ the 99 percent confidence interval for p.
A) wider than
B) narrower than
C) equal to

Accepted Answer

A 90 percent confidence interval is narrower than a 99 percent confidence interval because a lower confidence level requires less margin for error.

Question 6

A confidence interval for the population mean is meant to contain a specified percentage of the individual population measurements.

Accepted Answer

A confidence interval is a range of values derived from a sample that is likely to include the true population parameter with a certain level of confidence. It is not intended to contain a specified percentage of individual population measurements.

Question 7

When determining the sample size,if the value found is not an integer initially,you should ____________ choose the next highest integer value.
A) always
B) sometimes
C) never

Accepted Answer

Sample sizes should always be rounded up to the next highest integer value to ensure that there are enough participants to provide reliable results.

Question 8

The width of a confidence interval will be
A) narrower for 98 percent confidence than for 90 percent confidence.
B) wider for a sample size of 64 than for a sample size of 36.
C) wider for 99 percent confidence than for 95 percent confidence
D) narrower for a sample size of 25 than for a sample size of 36.
E) None of the other choices is correct.

Accepted Answer

A higher confidence level (e.g., 99% vs. 95%) results in a wider confidence interval because it requires more certainty, thus a larger margin of error.

Question 9

A tolerance interval is always longer than a corresponding confidence interval.

Accepted Answer

A tolerance interval is a range that is expected to contain a certain proportion of the population with a certain level of confidence, whereas a confidence interval is a range that is expected to contain the true population parameter with a certain level of confidence. Since the tolerance interval includes the variability of the population, it is wider than a corresponding confidence interval that only considers the variability of the sample.

Question 10

A tolerance interval is meant to contain a specified percentage of the individual population measurements.

Accepted Answer

A tolerance interval is a statistical interval that is intended to contain a specified percentage of the population measurements with a specified level of confidence. Unlike a confidence interval that estimates a population parameter, a tolerance interval gives a range of values that covers a specified proportion of the population observations.

Question 11

Which of the following is an advantage of a confidence interval estimate over a point estimate for a population parameter?
A) Interval estimates are more precise than point estimates.
B) Interval estimates are less accurate than point estimates.
C) Interval estimates are both more accurate and more precise than point estimates.
D) Interval estimates take into account the fact that the statistic being used to estimate the population parameter is a random variable.

Accepted Answer

A confidence interval takes into account the fact that the statistic being used to estimate the population parameter is a random variable, whereas a point estimate does not. This means that a confidence interval provides a range of values within which the true population parameter is likely to fall, whereas a point estimate provides only a single value. Therefore, a confidence interval estimate is generally more accurate than a point estimate. However, the precision of the estimate depends on the width of the interval, with narrower intervals being more precise than wider intervals.

Question 12

The t distribution approaches the _______________ distribution as the sample size ___________.
A) binomial,increases
B) binomial,decreases
C) z,decreases
D) z,increases

Accepted Answer

The t distribution approaches the normal (z) distribution as the sample size increases. This is because as the sample size increases, the distribution of sample means becomes more normal in shape (according to the Central Limit Theorem), and the standard error of the mean decreases. As a result, the t distribution becomes more similar to the standard normal distribution (z), with a mean of 0 and standard deviation of 1.

Question 13

The width of a confidence interval will be
A) narrower for 99 percent confidence than for 95 percent confidence.
B) wider for a sample size of 100 than for a sample size of 50.
C) narrower for 90 percent confidence than for 95 percent confidence.
D) wider when the sample standard deviation (s)is small than when s is large.

Accepted Answer

You have a 10% chance of being wrong with a 90% confidence interval and a 5% chance of being wrong with a 95% confidence interval.

Question 14

When the level of confidence and sample size remain the same,a confidence interval for a population proportion,p,will be ______________ when is larger than when 
Is smaller.
A) wider
B) narrower
C) neither wider nor narrower (they will be the same)

Accepted Answer

The margin of error of a confidence interval for a population proportion is directly proportional to the square root of (p(1-p)/n), where p is the sample proportion and n is the sample size. If the sample size remains the same but the population proportion increases (i.e. p is larger), the margin of error will also increase, resulting in a wider confidence interval. Conversely, if the population proportion decreases (i.e. p is smaller), the margin of error will decrease, resulting in a narrower confidence interval. Therefore, the answer is A.

Question 15

A confidence interval increases in width as
A) the level of confidence increases.
B) n decreases.
C) s increases.
D) All of the other choices are correct.

Accepted Answer

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the interval is determined by several factors, including the level of confidence, sample size (n), and sample standard deviation (s). As the level of confidence increases, the range of values that could contain the true parameter widens, resulting in a wider confidence interval. A smaller sample size (n) leads to greater uncertainty and wider intervals. A higher standard deviation (s) indicates more variability in the sample, and therefore a wider interval. Therefore, all of the other choices are correct.

Question 16

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion p,having a given error bound E,we choose a value of that
A) makes 
As small as reasonably possible.
B) makes 
As large as reasonably possible.
C) makes 
As close to .5 as reasonably possible.
D) makes 
As close to .25 as reasonably possible.
E) makes

Accepted Answer

The answer of When solving for the sample size needed...

Question 17

When the level of confidence and sample proportion remain the same,a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.
A) wider than
B) narrower than
C) equal to

Accepted Answer

A confidence interval is wider for smaller sample sizes. Since n = 100 is smaller than n = 400, the confidence interval for n = 100 will be wider.

Question 18

When the level of confidence and sample standard deviation remain the same,a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.
A) wider than
B) narrower than
C) equal to

Accepted Answer

With a larger sample size, there is less error in estimating the population parameter.

Question 19

When the sample size and sample standard deviation remain the same,a 99 percent confidence interval for a population mean,μ,will be _________________ the 95 percent confidence interval for μ.
A) wider than
B) narrower than
C) equal to

Accepted Answer

A 99 percent confidence interval will be wider than a 95 percent confidence interval because it includes more of the population's values, which increases the margin of error.

Question 20

When the level of confidence and the sample size remain the same,a confidence interval for a population mean μ will be ________________ when the sample standard deviation s is small than when s is large.
A) wider
B) narrower
C) neither wider nor narrower (they will be the same)

Accepted Answer

When the sample standard deviation is smaller, it means that the data points are closer to the mean. This results in a more precise estimate of the population mean, leading to a narrower confidence interval. Conversely, when the sample standard deviation is larger, the data points are more spread out, which leads to a less precise estimate of the population mean and a wider confidence interval. However, it is important to note that changing the sample size or level of confidence will also affect the width of the confidence interval.

Quiz 8: Confidence Intervals

The exact spread of the t distribution depends on the _________.

As standard deviation increases,sample size _____________ to achieve a specified level of confidence.

When constructing a confidence interval for a population mean,if a population is normally distributed and a small sample is taken,then the distribution of is based on the ____________ distribution.

When the population is normally distributed,population standard deviation σ is unknown,and the sample size is n = 15,the confidence interval for the population mean μ is based on

When the sample size and the sample proportion remain the same,a 90 percent confidence interval for a population proportion p will be ______________ the 99 percent confidence interval for p.

A confidence interval for the population mean is meant to contain a specified percentage of the individual population measurements.

When determining the sample size,if the value found is not an integer initially,you should ____________ choose the next highest integer value.

The width of a confidence interval will be

A tolerance interval is always longer than a corresponding confidence interval.

A tolerance interval is meant to contain a specified percentage of the individual population measurements.

Which of the following is an advantage of a confidence interval estimate over a point estimate for a population parameter?

The t distribution approaches the _____ distribution as the sample size _.

The width of a confidence interval will be

When the level of confidence and sample size remain the same,a confidence interval for a population proportion,p,will be ______________ when is larger than when 11ec8fec_dcc7_868b_bdf7_b7e05f5c77bd_TB2569_11 Is smaller.

A confidence interval increases in width as

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion p,having a given error bound E,we choose a value of that

When the level of confidence and sample proportion remain the same,a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.

When the level of confidence and sample standard deviation remain the same,a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.

When the sample size and sample standard deviation remain the same,a 99 percent confidence interval for a population mean,μ,will be _________________ the 95 percent confidence interval for μ.

When the level of confidence and the sample size remain the same,a confidence interval for a population mean μ will be ________________ when the sample standard deviation s is small than when s is large.