Chapter 6 Sampling Distributions and Confidence Intervals

In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be __________ degrees of freedom.

11

A 99% confidence interval estimate can be interpreted to mean that:

If all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. You have 99% confidence that you have selected a sample whose interval does include the population mean.

For samples of n = 1, the sampling distribution of the mean will be normally distributed:

If the population is normally distributed.

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

It has a normal distribution with the same mean as the population.

The Central Limit Theorem is important in statistics because:

It states that the sampling distribution of the sample mean is approximately normally distributed for a large sample size n regardless of the shape of the population.

As an aid to the establishment of personnel requirements, the manager of a bank wants to estimate the mean number of people who arrive at the bank during the two-hour lunch period from 12 noon to 2 p.m. The director randomly selects 64 different two-hour lunch periods from 12 noon to 2 p.m. and determines the number of people who arrive for each. For the sample, x̅ = 49.8 and S = 5. Which assumption is necessary in order for a confidence interval to be valid? a) The population sampled from has an approximate normal distribution. b) The population sampled from has an approximate t distribution. c) The mean of the sample equals the mean of the population. d) none of these

None of these assumptions is necessary.

A university dean is interested in determining the proportion of students who are planning to attend graduate school. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are planning to attend graduate school. The 95% confidence interval for p is 0.59 ± 0.07. Interpret this interval.

You are 95% confident that the true proportion of all students planning to attend graduate school is between 0.52 and 0.66.

The sampling distribution of the mean requires ___________ sample size to reach a normal distribution if the population is skewed than if the population is symmetrical.

a larger

The sampling distribution of the mean can be approximated by the normal distribution:

as the sample size (number of observations in each sample) gets large enough

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population. (true or false)

false

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a wider interval. (true or false)

false

The confidence interval estimate that is constructed will always correctly estimate the population parameter. (true or false)

false

You can construct a 100% confidence interval estimate of μ.

false

For samples of n = 15, the sampling distribution of the mean will be normally distributed:

if the shape of the population is symmetrical.

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a _____________ interval.

narrower

For samples of n = 30, for most populations, the sampling distribution of the mean will be approximately normally distributed:

regardless of the shape of the population

Sampling distributions describe the distribution of:

statistics

Alpha (α) is the proportion in the tails of the distribution that is outside the confidence interval.

true

As the sample size increases, the effect of an extreme value on the sample mean becomes smaller. (true or false)

true

In practice, the population mean is the unknown quantity that is to be estimated.

true

Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases. (true or false)

true

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown. (true or false)

true

There is a different critical value for each level of alpha (α) True of false?

true