Business Statistics - Chapter 8: Interval Estimation Quiz

The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 - p) equal or exceed _____. a) 5 b) .05 c) 30 d) 15

a) 5

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____. a) becomes narrower b) becomes .1 c) does not change d) becomes wider

a) becomes narrower

The mean of the t distribution is _____. a) 1 b) .5 c) 0 d) dependent upon the sample size

c) 0

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is _____. a) 19.2 to 20.8 b) 15.2 to 24.8 c) 19.216 to 20.784 d) 21.2 to 22.8

a) 19.2 to 20.8

The t value with a 95% confidence and 24 degrees of freedom is _____. a) 2.064 b) 2.069 c) 2.492 d) 1.7111

a) 2.064

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____. a) becomes smaller b) becomes larger c) stays the same d) None of these answers are correct.

a) becomes smaller

When the level of confidence increases, the confidence interval _____. a) becomes wider b) stays the same c) becomes narrower d) Cannot be determined from the information given.

a) becomes wider

The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____. a) confidence coefficient b) confidence level c) level of significance d) error factor

a) confidence coefficient

As the sample size increases, the margin of error _____. a) decreases b) increases c) stays the same d) None of these answers are correct.

a) decreases

Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean? a) t distribution b) binomial distribution c) standard distribution d) z distribution

a) t distribution

In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed? a) the mean of the population b) the maximum margin of error that can be tolerated c) the confidence level required d) a preliminary estimate of the true population proportion p

a) the mean of the population

From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for μ. Which of the following statements is true? a) The t distribution with 50 degrees of freedom must be used. b) The t distribution with 49 degrees of freedom must be used. c) The sample size must be increased in order to develop an interval estimate. d) The standard normal distribution can be used.

b) The t distribution with 49 degrees of freedom must be used.

An interval estimate is used to estimate _____. a) a sample statistic b) a population parameter c) the shape of the population's distribution d) the sampling distribution

b) a population parameter

The ability of an interval estimate to contain the value of the population parameter is described by the _____. a) degrees of freedom b) confidence level c) precise value of the population mean μ d) None of these answers are correct.

b) confidence level

In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom. a) √n-1 b) n - 1 c) n d) √n

b) n - 1

For the interval estimation of μ when σ is assumed known, the proper distribution to use is the_____. a) t distribution with n degrees of freedom b) standard normal distribution c) t distribution with n − 2 degrees of freedom d) t distribution with n − 1 degrees of freedom

b) standard normal distribution

We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT _____. a) increasing the sample size b) using a planning value p* closer to .5 c) increasing the level of significance d) reducing the confidence coefficient

b) using a planning value p* closer to .5

If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____. a) x̄ ± 4.508 b) x̄ ± 4.6 c) x̄ ± 2.3 d) x̄ ± 6.9

b) x̄ ± 4.6

The z value for a 97.8% confidence interval estimation is _____. a) 1.96 b) 2.02 c) 2.29 d) 2.00

c) 2.29

A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is _____. a) 70.02 to 81.98 b) 69.82 to 82.18 c) 69.29 to 82.71 d) 70.06 to 81.94

c) 69.29 to 82.71

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the _____. a) finite correction factor b) standard deviation c) degrees of freedom d) sample size

c) degrees of freedom

An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the _____. a) parameter value b) population estimate c) interval estimate d) confidence level

c) interval estimate

The t distribution should be used whenever _____. a) the population is not normally distributed b) the same size is less than 30 c) the sample standard deviation is used to estimate the population standard deviation d) None of these answers are correct.

c) the sample standard deviation is used to estimate the population standard deviation

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____. a) whether the population has an approximately normal distribution b) whether the population standard deviation is known c) whether there is sampling error d) the sample size

c) whether there is sampling error

In general, higher confidence levels provide _____. a) unbiased estimates b) narrower confidence intervals c) wider confidence intervals d) smaller standard error

c) wider confidence intervals

Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for p̄. In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size for a given level of confidence and a given margin of error is a) 1 b) .10 c) .90 d) .50

d) .50

To estimate a population mean, the sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is _____. a) 10 b) 11 c) 116 d) 117

d) 117

The confidence associated with an interval estimate is called the _____. a) level of significance b) precision c) degree of association d) confidence level

d) confidence level

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____. a) confidence level b) desired margin of error c) population standard deviation d) degrees of freedom

d) degrees of freedom

The general form of an interval estimate of a population mean or population proportion is the _____ plus or minus the _____. a) level of significance, degrees of freedom b) population mean, standard error c) planning value, confidence coefficient d) point estimate, margin of error

d) point estimate, margin of error