Chapter 5 Sampling Distributions and Interval, 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

According to the text, the shape of the sampling distribution of the statistic p hat is

Approximately normal if the sample size n is 'large'

Which of the following best describes the Central Limit Theorem? The Central Limit Theorem describes the

Shape of the sampling distribution of the statistic x bar

What actions would you take in order to generate a more precise interval estimate?

Take a larger sample

Which of the following best describes the mean of the sampling distribution of the statistic x bar?

Take all possible samples of n=30 observations from the population. Calculate the mean of each sample, then calculate the mean of the sample means

Which of the following is correct regarding the margin for error?

The margin of error is the quantity that is added to and subtracted from a point estimate of a population parameter to obtain a confidence interval for the parameter

Which of the following best describes the mean of the sampling distribution of the statistic p hat?

The mean of the sample proportions (p hat) calculated from all possible samples of a certain size n drawn from a specified population

Suppose a sampling distribution of the statistic x bar is generated from two possible sample sizes; 30 and 60. Which statement best describes the effect on the sampling distribution of the statistic x bar as the sample size increases from 30 up to 60?

The mean of the sampling distribution of the statistic x bar does not change

Which of the following best describes the definition of the sampling distribution of the sample mean?

The probability distribution of the population of all sample means obtained from samples of a particular size n

Other things held equal, the larger the sample size

The smaller the margin for error

Which of the following best describes the standard deviation of the sampling distribution of the statistic p hat?

The square root of the result when you take the (population proportion p multiplied by (1 minus p)) divided by the sample size n

How does the t-distribution differ from the z-distribution?

The t-distribution is symmetrical about zero but is spread out more than a standard normal curve

Suppose you do not know the population standard deviation but you do know that the shape of the population is normal. How would you go about calculating a confidence interval for the population mean?

Use the point estimator +/- t times the standard error of the mean

When would you use the t-distribution to calculate a confidence interval for the population mean?

When estimating the population mean with an unknown sigma but a population that is normally distributed

Which of the following best describes the definition of the unbiasedness property?

When the mean of the population of all possible values of the sample statistic equals the corresponding population parameter

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

Which of the following is true if you wish to obtain a confidence interval for a population mean?

the larger the sample size, the more precise the interval estimate

Sampling distributions describe the distribution of:

statistics

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.

How large does n have to be in order to assume normality of the sampling distribution of the statistic p hat?

Large enough so that both np and n(1-p) are at least 15

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?

None of these assumptions is necessary.

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

The probability that a confidence interval for a population parameter will contain the population parameter is defined as the

confidence coefficient

The percentage of time that a confidence interval would contain a population parameter if all possible samples were used to calculate the interval is defined as the

confidence level

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

if the shape of the population is symmetrical.

Out of the class of all unbiased point estimators for a population parameter, the preferred point estimator is the one that has

minimum variance

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