qmb exam1 ch8

margin of error

The ± value added to and subtracted from a point estimate in order to develop an interval estimate of a population parameter.

We can reduce the margin of error in an interval estimate of p by doing any of the following except:

increasing the sample size. increasing the level of significance. reducing the confidence coefficient. {{increasing the planning value p* to .5.}}

For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval:

must be larger.

The sampling distribution of p^ can be approximated by a normal distribution as long as:

np>=5 and n(1-p)>=5

When "s" is used to estimate "σ," the margin of error is computed by using the:

t distribution

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except:

using the estimated σ from a previous study. using judgment or a best guess. {{using σ = 1.}} using the sample standard deviation from a preliminary sample.

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except:

using the sample proportion from a previous study. {{using .95 as an estimate.}} using judgment or a best guess. using the sample proportion from a preliminary sample.

When computing the sample size needed to estimate a proportion within a given margin of error for a specific confidence level, what planning value of p should be used when no estimate of p is available?

0.50

Suppose a 95% confidence interval, based upon a sample of size 25, for the mean number of hours of sleep that college students get per night was 5 to 8 hours. How many students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours?

100

In an interval estimation for a proportion of a population, the critical value of z at 99% confidence is:

2.576

degrees of freedom

A parameter of the t distribution. When the t distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n − 1 degrees of freedom, where n is the size of the sample.

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. Which of the following statements is true?

A t distribution should be used because σ is unknown.

Confidence interval (interval estimate)

An estimate of a population parameter that provides an interval believed to contain the value of the parameter. For the interval estimates in this chapter, it has the form: point estimate ± margin of error.

An elementary school teacher asked a random sample of 12 of her students what their favorite number was. Assume the population of responses would follow a normal distribution. The students stated that their favorite numbers are: Suppose we were to create a 95% confidence interval for μ. What effect does the value 100 have on the width of the confidence interval?

It makes the interval wider.

confidence level

The confidence associated with an interval estimate. For example, if an interval estimation procedure provides intervals such that 95% of the intervals formed using the procedure will include the population parameter, the interval estimate is said to be constructed at the 95% confidence level.

confidence coefficient

The confidence level expressed as a decimal value. For example, .95 is the confidence coefficient for a 95% confidence level.

In interval estimation, as the sample size becomes larger, the interval estimate:

becomes narrower.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution:

becomes smaller.

When the level of confidence decreases, the margin of error:

becomes smaller.

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion:

becomes wider.

As the sample size increases, the margin of error:

decreases.

If the population follows a normal distribution, the confidence interval is _____ and can be used for any sample size. If the population does not follow a normal distribution, the confidence interval will be _____. Which of the following choices correctly complete this statement?

exact; approximate.

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is:

four times as large as the original sample size.

In general, higher confidence levels provide larger confidence intervals. One way to have high confidence and a small margin of error is to:

increase the sample size.

An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known as the:

interval estimate.

The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the:

level of significance.

The margin of error in an interval estimate of the population mean is a function of all of the following except the:

level of significance. sample size. variability of the population. {{sample mean.}}

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the:

margin of error.

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is:

nine times as large as the original sample size.

From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the:

t distribution with 29 degrees of freedom.

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is:

the normal distribution