Business Statistics Final chpt 8-10

The ability of an interval estimate to contain the value of the population parameter is described by the a. confidence level. b. degrees of freedom. c. precise value of the population mean μ. d. point estimate.

a. confidence level.

As the test statistic becomes larger, the p-value a. gets smaller. b. becomes larger. c. goes beyond 1. d. becomes negative

a. gets smaller.

In hypothesis tests about a population proportion, p0 represents the a. hypothesized population proportion. b. observed sample proportion. c. observed p-value. d. probability that H0 is correct

a. hypothesized population proportion.

A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the a. normal distribution. b. t distribution with 200 degrees of freedom. c. t distribution with 201 degrees of freedom. d. t distribution with 199 degrees of freedom

a. normal distribution.

The sampling distribution of pvar1-pvar2 is approximated by a a. normal distribution. b. t distribution with n1 + n2 degrees of freedom. c. t distribution with n1 + n2 - 1 degrees of freedom. d. pvar1-pvar2 distribution

a. normal distribution.

The mean of the t distribution is a. 0. b. .5. c. 1. d. problem specific.

a. 0.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic a. at least as small as that provided by the sample. b. at least as large as that provided by the sample. c. at least as small as that provided by the population. d. at least as large as that provided by the population.

a. at least as small as that provided by the sample.

A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are a. H0: μ ≠ 5.8 Ha: μ = 5.8. b. H0: μ = 5.8 Ha: μ ≠ 5.8. c. H0: μ > 5.8 Ha: μ ≤ 5.8. d. H0: μ ≥ 5.8 Ha: μ < 5.8.

b. H0: μ = 5.8 Ha: μ ≠ 5.8.

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is a. H0: p < .35 Ha: p .35. b. H0: p .35 Ha: p > .35. c. H0: p .35 Ha: p < .35. d. H0: p > .35 Ha: p .35.

c. H0: p .35 Ha: p < .35.

The standard error of xvar1-xvar2 is the a. pooled estimator of xvar1-xvar2 . b. variance of the sampling distribution of xvar1-xvar2 . c. standard deviation of the sampling distribution of xvar1-xvar2. d. margin of error of xvar1-xvar2.

c. standard deviation of the sampling distribution of

Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. None of these alternatives is correct

c. the level of significance

In developing an interval estimate, if the population standard deviation is unknown a. it is impossible to develop the interval estimate. b. the standard deviation is arrived at using the range. c. the sample standard deviation must be used. d. it is assumed that the population standard deviation is 1.

c. the sample standard deviation must be used.

To compute the minimum sample size for an interval estimate of l , we must first determine all of the following except a. desired margin of error. b. confidence level. c. population standard deviation. d. degrees of freedom.

d. degrees of freedom.

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a. corresponding samples. b. matched samples. c. independent samples. d. pooled samples.

b. matched samples.

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

a. wider confidence intervals.

Two approaches to drawing a conclusion in a hypothesis test are a. p-value and critical value. b. one-tailed and two-tailed. c. Type I and Type II. d. null and alternative.

a. p-value and critical value.

When the null hypothesis is rejected, it is a. possible a Type I error has occurred. b. not possible a Type I error has occurred. c. possible a Type II error has occurred. d. possible either a Type I or a Type II error has occurred.

a. possible a Type I error has occurred.

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the a. width of the confidence interval to increase. b. width of the confidence interval to decrease. c. width of the confidence interval to remain the same. d. sample size to increase.

a. width of the confidence interval to increase.

f the null hypothesis is not rejected at the 5% level of significance, it a. will also not be rejected at the 1% level. b. will always be rejected at the 1% level. c. will sometimes be rejected at the 1% level. d. may be rejected or not rejected at the 1% level.

a. will also not be rejected at the 1% level.

When the following hypotheses are being tested at a level of significance of α H0: μ 500 Ha: μ < 500 the null hypothesis will be rejected, if the p-value is a. α. b. > α. c. = α/2. d. 1 - α/2.

a. α.

A Type I error is committed when a. a true alternative hypothesis is not accepted. b. a true null hypothesis is rejected. c. the critical value is greater than the value of the test statistic. d. sample data contradict the null hypothesis.

b. a true null hypothesis is rejected.

If the null hypothesis is rejected at the .05 level of significance, it will a. always not be rejected at the .10 level of significance. b. always be rejected at the .10 level of significance. c. sometimes be rejected at the .10 level of significance. d. sometimes not be rejected at the .10 level of significance.

b. always be rejected at the .10 level of significance.

When the level of confidence decreases, the margin of error a. stays the same. b. becomes smaller. c. becomes larger. d. becomes smaller or larger, depending on the sample mean

b. becomes smaller

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 larger. b. becomes smaller. c. stays the same. d. fluctuates.

b. becomes smaller.

. Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion a. becomes narrower. b. becomes wider. c. uses a zero margin of error. d. remains the same.

b. becomes wider.

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. increasing the planning value p* to .5. c. increasing α. d. reducing the confidence level

b. increasing the planning value p* to .5.

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

b. interval estimate.

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve a. less than or equal to the critical value. b. less than or equal to the test statistic. c. greater than or equal to the critical value. d. greater than or equal to the test statistic.

b. less than or equal to the test statistic.

the level of significance is the a. maximum allowable probability of Type II error. b. maximum allowable probability of Type I error. c. same as the confidence coefficient. d. same as the p-value.

b. maximum allowable probability of Type I error.

In hypothesis testing if the null hypothesis is rejected, a. no conclusions can be drawn from the test b. the alternative hypothesis is true c. the data must have been accumulated incorrectly d. the sample size has been too small

b. the alternative hypothesis is true

If the null hypothesis is rejected in hypothesis testing, a. no conclusions can be drawn from the test. b. the alternative hypothesis is true. c. the data must have been accumulated incorrectly. d. the sample size has been too small

b. the alternative hypothesis is true.

In hypothesis testing, the tentative assumption about the population parameter is a. the alternative hypothesis. b. the null hypothesis. c. either the null or the alternative. d. neither the null nor the alternative.

b. the null hypothesis.

The t distribution should be used whenever a. the sample size is less than 30. b. the sample standard deviation is used to estimate the population standard deviation. c. the population is not normally distributed. d. the population standard deviation is known.

b. the sample standard deviation is used to estimate the population standard deviation.

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as a. likely as that provided by the sample. b. unlikely as that provided by the sample. c. likely as that provided by the population. d. unlikely as that provided by the population.

b. unlikely as that provided by the sample.

. In hypothesis tests about p1 - p2, the pooled estimator of p is a(n) a. simple average of and pvar1 and pvar2. b. weighted average of pvar1 and pvar2 . c. geometric average of pvar1 and pvar2 . d. exponential average of pvar1 and pvar2.

b. weighted average of pvar1 and pvar2 .

If a hypothesis is rejected at 95% confidence, it a. will not be rejected at 90% confidence b. will also be rejected at 90% confidence c. will sometimes be rejected at 90% confidence d. None of these alternatives is correct

b. will also be rejected at 90% confidence

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to a. α. b. α/2. c. 2α. d. 1 - α/2.

b. α/2.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the a. null hypothesis should state p1 - p2 < 0. b. null hypothesis should state p1 - p2 > 0. c. alternative hypothesis should state p1 - p2 > 0. d. alternative hypothesis should state p1 - p2 < 0.

c. alternative hypothesis should state p1 - p2 > 0. d

If we are interested in testing whether the mean of items in population 1 is larger than the mean of items in population 2, the a. null hypothesis should state μ1 - μ2 < 0 b. null hypothesis should state μ1 - μ2 > 0 c. alternative hypothesis should state μ1 - μ2 > 0 d. alternative hypothesis should state μ1 - μ2 < 0

c. alternative hypothesis should state μ1 - μ2 > 0

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a. can be approximated by any distribution. b. will have a variance of one. c. can be approximated by a normal distribution. d. will have a mean of one.

c. can be approximated by a normal distribution.

For the following hypothesis test, H0: μ ≥ 150 Ha: μ < 150 the test statistic a. must be negative. b. must be positive. c. can be either negative or positive. d. must be a number between zero and one.

c. can be either negative or positive.

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on a. research samples. b. pooled samples. c. independent samples. d. conditional samples

c. independent samples.

If the cost of making a Type I error is high, a smaller value should be chosen for the a. critical value. b. confidence coefficient. c. level of significance. d. test statistic.

c. level of significance.

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach. a. single, independent b. independent, pooled c. matched, independent d. matched, pooled

c. matched, independent

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ). a. The normal distribution can be used. b. The t distribution with 5 degrees of freedom must be used. c. The t distribution with 6 degrees of freedom must be used. d. The sample size must be increased.

d. The sample size must be increased.

The p-value a. is the same as the Z statistic b. measures the number of standard deviations from the mean c. is a distance d. is a probability

d. is a probability

The sum of the values of α and β a. is always 1. b. is always .5. c. gives the probability of taking the correct decision. d. is not needed in hypothesis testing.

d. is not needed in hypothesis testing.

Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on a. worker samples. b. pooled samples. c. independent samples. d. matched samples

d. matched samples

30. If the null hypothesis is rejected at the 5% level of significance, it a. will always be rejected at the 1% level. b. will always not be rejected at the 1% level. c. will never be tested at the 1% level. d. may be rejected or not rejected at the 1% level.

d. may be rejected or not rejected at the 1% level.

When developing an interval estimate for the difference between two population means with sample sizes of n1 and n2, a. n1 must be equal to n2. b. n1 must be smaller than n2. c. n1 must be larger than n2. d. n1 and n2 can be of different sizes.

d. n1 and n2 can be of different sizes.

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. Let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is a. pu - po ≤ 0. b. pu - po ≥ 0. c. pu - po ≠ 0. d. pu - po = 0.

d. pu - po = 0.

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the a. proportion estimate. b. margin of error. c. confidence coefficient. d. same as α

d. same as α

From a population that is normally distributed, a sample of 25 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 a. normal distribution. b. t distribution with 25 degrees of freedom. c. t distribution with 26 degrees of freedom. d. t distribution with 24 degrees of freedom

d. t distribution with 24 degrees of freedom

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, a. a Type I error has been committed. b. a Type II error has been committed. c. either a Type I or a Type II error has been committed. d. the correct decision has been made

d. the correct decision has been made

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 a. use the estimated σ from a previous study. b. use the sample standard deviation from a preliminary sample. c. use judgment or a best guess. d. use .5 as an estimate

d. use .5 as an estimate