STATS REEE
. In a regression and correlation analysis, if r2 = 1, then a. SSE must also be equal to one. b. SSE must be equal to zero. c. SSE can be any positive value. d. SSE must be negative.
b
. It is possible for the coefficient of determination to be a. larger than 1. b. less than 1. c. less than -1. d. equal to -1.
b
= 8.231 indicates that a. 97.5% of the chi-square values are less than 8.231. b. 97.5% of the chi-square values are greater than 8.231. c. 2.5% of the chi-square values are greater than 8.231. d. 5% of the chi-square values are equal to 8.231.
b
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 sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are a. 27.99 and 79.49. b. 32.357 and 71.420. c. 34.764 and 67.505. d. 12.8786 and 46.9630.
b
A sample of n observations is taken from a normal population. The appropriate chi-square distribution has a. n degrees of freedom. b. n - 1 degrees of freedom. c. n - 2 degrees of freedom. d. n - 3 degrees of freedom.
b
A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .09. The null hypothesis a. must be rejected. b. should not be rejected. c. could be rejected, depending on the sample size. d. has been designed incorrectly.
b
As a general guideline, the research hypothesis should be stated as the a. null hypothesis. b. alternative hypothesis. c. tentative hypothesis. d. hypothesis the researcher wants to disprove.
b
Given the following information, n = 49, = 50, s = 7 H0: μ > 52 Ha: μ < 52 the test statistic is a. 2. b. -2. c. 1. d. -1.
b
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
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
. A sample of 20 cans of tomato juice showed a standard deviation of .4 ounces. A 95% confidence interval estimate of the variance for the population is a. .2313 to .8533. b. .2224 to .7924. c. .3042 to .5843. d. .0925 to .3413.
d
. In regression analysis, if the independent variable is measured in pounds, the dependent variable a. must also be in pounds. b. must be in some unit of weight. c. cannot be in pounds. d. can be measured in any units.
d
. Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) using α = .1230, z = a. 1.54. b. 1.96. c. 1.645. d. 1.16.
d
. The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as a. H0: σ2 ≥ .05. b. H0: σ2 > .05. c. H0: σ2 < .05. d. H0: σ2 ≤ .05.
d
. 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
A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is a. 100.75. b. 10. c. 51.25. d. 50.
d
For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis a. could be rejected or not rejected depending on the sample size. b. could be rejected or not rejected depending on the sample mean. c. is not rejected. d. is rejected.
d
For a two-tailed hypothesis test about , we can use any of the following approaches except a. compare the confidence interval estimate of to the hypothesized value of b. compare the p-value to the value of c. compare the value of the test statistic to the critical value. d. compare the level of significance to the confidence coefficient.
d
For an F distribution, the number of degrees of freedom for the numerator a. must be larger than the number of degrees of freedom for the denominator. b. must be smaller than the number of degrees of freedom for the denominator. c. must be equal to the number of degrees of freedom for the denominator. d. can be larger, smaller, or equal to the number of degrees of freedom for the denominator.
d
If a hypothesis test leads to the rejection of the null hypothesis, a. a Type II error must have been committed. b. a Type II error may have been committed. c. a Type I error must have been committed. d. a Type I error may have been committed.
d
If the coefficient of correlation is a negative value, then the coefficient of determination a. must also be negative. b. must be zero. c. can be either negative or positive. d. will be positive.
d
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
If the probability of a Type I error (α) is .05, then the probability of a Type II error (β) must be a. .05. b. .95. c. .025. d. Cannot be computed.
d
If there is a very strong correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive. b. much smaller than -1, if the correlation is negative. c. equal to zero. d. closer or equal to 1.
d
If there is a very weak correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive. b. much smaller than -1, if the correlation is negative. c. equal to one. d. closer or equal to zero.
d
In a regression and correlation analysis, if r2 = 1, then a. SSE = SST. b. SSE = 1. c. SSR = SSE. d. SSR = SST.
d
In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then a. there is a positive correlation between x and y. b. if x is increased, y must also increase. c. if y is increased, x must also increase. d. the estimated regression line intercepts the positive y-axis.
d
In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.692. The sample size has been 45. The p-value for this test is a. -.005. b. +.005. c. -.01. d. +.01.
d
The probability of making a Type II error is denoted by a. α. b. β. c. 1 - α. d. 1 - β.
b
The symbol used for the variance of the sample is a. σ. b. σ2. c. s. d. s2.
d
. 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
. In regression and correlation analysis, if SSE and SST are known, then with this information the a. coefficient of determination can be computed. b. slope of the regression line can be computed. c. y-intercept can be computed. d. x-intercept can be computed.
a
. In the hypothesis testing procedure, α is the a. level of significance. b. critical value. c. confidence level. d. p-value.
a
. The value of the coefficient of correlation (r) a. can be equal to the value of the coefficient of determination (r2). b. can never be equal to the value of the coefficient of determination (r2). c. is always smaller than the value of the coefficient of determination (r2). d. is always larger than the value of the coefficient of determination (r2).
a
. What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one-tailed or two-tailed
a
. 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
A Type II error is committed when a. a true alternative hypothesis is mistakenly rejected. b. a true null hypothesis is mistakenly rejected. c. the true null hypothesis is correctly rejected. d. the true alternative hypothesis is correctly rejected.
a
A least squares regression line a. can be used to predict a value of y if the corresponding x value is given. b. implies a cause-and-effect relationship between x and y. c. can only be determined if a good linear relationship exists between x and y. d. ensures that the predictions of y outside the range of the values of x are valid.
a
A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is a. 20. b. 21. c. 5. d. 50.
a
An assumption made about the value of a population parameter is called a(n) a. hypothesis. b. conclusion. c. error. d. probability.
a
As the test statistic becomes larger, the p-value a. gets smaller. b. becomes larger. c. goes beyond 1. d. becomes negative.
a
Compared to the confidence interval estimate for a particular value of y in a linear regression model, the interval estimate for an average value of y will be a. narrower. b. wider. c. the same. d. easy to determine.
a
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
For a sample size of 21 at 95% confidence, the chi-square values needed for interval estimation are a. 9.591 and 34.170. b. 2.700 and 19.023. c. 8.260 and 37.566. d. 10.283 and 35.479.
a
If 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
In hypothesis testing, the critical value is a. a number that establishes the boundary of the rejection region. b. the probability of a Type I error. c. the probability of a Type II error. d. the same as the p-value.
a
In order to test the following hypotheses at an α level of significance H0: μ 800 Ha: μ > 800 the null hypothesis will be rejected, if the test statistic z is a. zα. b. < zα. c. < -zα. d. = α.
a
In regression analysis, the variable that is being predicted is the a. dependent variable. b. independent variable. c. intercept variable. d. error variable.
a
In regression analysis, which of the following assumptions is not true about the error term ε? a. The expected value of the error term is one. b. The variance of the error term is the same for all values of x. c. The values of the error term are independent. d. The error term is normally distributed.
a
In the following estimated regression equation = b0 + b1x, a. b1 is the slope. b. b1 is the intercept. c. b1x is the slope. d. b1x is the intercept.
a
SSE can never be a. larger than SST. b. smaller than SST. c. equal to one. d. equal to zero.
a
The coefficient of determination a. cannot be negative. b. is the square root of the coefficient of correlation. c. is the same as the coefficient of correlation. d. can be negative or positive.
a
The error of rejecting a true null hypothesis is a. a Type I error. b. a Type II error. c. always negligible in hypothesis testing. d. never committed in hypothesis testing.
a
The interval estimate of an individual value of y for a given value of x is the a. prediction interval estimate. b. confidence interval estimate. c. average regression interval. d. x versus y correlation interval.
a
The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is a. 8.576 to 39.794. b. 9.46 to 34.09. c. 2.144 to 9.948. d. 2.93 to 6.31.
a
The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as the a. regression equation. b. correlation model. c. estimated regression equation. d. regression model.
a
The p-value is a probability that measures the support (or lack of support) for a. the null hypothesis. b. the alternative hypothesis. c. either the null or the alternative hypothesis. d. neither the null nor the alternative hypothesis.
a
The probability of making a Type I error is denoted by a. α. b. β. c. 1 - α. d. 1 - β.
a
The producer of a certain bottling equipment claims that the variance of all their filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2 ounces. The p-value for the test is a. between .025 to .05. b. between .05 to .10. c. .05. d. .025.
a
The sampling distribution of the quantity (n - 1)s2/σ2 is the a. chi-square distribution. b. normal distribution. c. F distribution. d. t distribution.
a
The value of F.05 with 8 numerator and 19 denominator degrees of freedom is a. 2.48. b. 2.58. c. 3.63. d. 2.96.
a
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
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
When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value α. b. p-value. c. p-value d. p-value .
a
When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value α. b. α < p-value. c. p-value = 1 - α/2. d. p-value = 1 - α.
a
. 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
. If the coefficient of determination is equal to 1, then the coefficient of correlation a. must also be +1. b. can be either -1 or +1. c. can be any value between -1 to +1. d. must be -1.
b
. 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
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
In practice, the most frequently encountered hypothesis test about a population variance is a a. one-tailed test, with rejection region in the lower tail. b. one-tailed test, with rejection region in the upper tail. c. two-tailed test, with equal-size rejection regions. d. two-tailed test, with unequal-size rejection regions.
b
In regression analysis, the independent variable is a. used to predict other independent variables. b. used to predict the dependent variable. c. the variable that is not used for prediction. d. the variable that is being predicted.
b
More evidence against H0 is indicated by a. lower levels of significance. b. smaller p-values. c. smaller critical values. d. lower probabilities for the power of the test.
b
Read the z statistic from the normal distribution table and circle the correct answer. For a two-tailed test using α = .1388, z = a. 1.96. b. 1.48. c. 1.09. d. .86.
b
The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is a. 33.196. b. 36.415. c. 39.364. d. 37.652.
b
The coefficient of correlation a. is the square of the r-square. b. is the square root of the r-square. c. can never be equal to r-square. d. can never be negative.
b
The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis a. should be rejected. b. should not be rejected. c. should be revised. d. should not be tested.
b
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called a. the correlation model. b. the regression model. c. correlation analysis. d. estimation analysis.
b
The interval estimate of the mean value of y for a given value of x is the a. prediction interval estimate. b. confidence interval estimate. c. average regression interval. d. x versus y correlation interval.
b
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
The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is a. 2.3. b. 22.99. c. 4.85. d. 24.2.
b
The symbol used for the variance of the population is a. σ. b. σ2. c. s. d. s2.
b
To compute an interval estimate for the difference between the means of two populations, the t distribution a. is restricted to small sample situations. b. is not restricted to small sample situations. c. can be applied when the populations have equal means. d. can be applied only when the populations have equal standard deviations.
b
We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is a. σ < 7. b. σ2 ≥ 7. c. σ < 49. d. σ2 ≥ 49.
b
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
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
When the null hypothesis is not rejected, it is a. possible a Type I error has occurred. b. possible a Type II error has occurred. c. not possible a Type II error has occurred. d. possible either a Type I or a Type II error has occurred.
b
. For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is a. zero. b. -.5. c. +.5. d. 1.
c
. In regression analysis, if the dependent variable is measured in dollars, the independent variable a. must also be in dollars. b. must be in some units of currency. c. can be measured in any units. d. cannot be in dollars.
c
. In regression analysis, the unbiased estimate of the variance is a. coefficient of correlation. b. coefficient of determination. c. mean square error. d. slope of the regression equation.
c
. The sampling distribution used when making inferences about a single population's variance is a. an F distribution. b. a t distribution. c. a chi-square distribution. d. a normal distribution.
c
. To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with a. the larger sample size. b. the smaller sample size. c. the larger sample variance. d. the smaller sample variance.
c
. To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the a. smaller sample variance be the numerator of the test statistic. b. larger sample variance be the numerator of the test statistic. c. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic. d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.
c
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
If only MSE is known, you can compute the a. r-square. b. coefficient of correlation. c. standard error. d. ith residual.
c
If the coefficient of correlation is -.4, then the slope of the regression line a. must also be -.4. b. can be either negative or positive. c. must be negative. d. must be .16.
c
If the coefficient of determination is a positive value, then the coefficient of correlation a. must also be positive. b. must be zero. c. can be either positive or negative. d. can be larger than 1.
c
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
If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will also increase from .01 to .05. b. will not change. c. will decrease. d. will increase.
c
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
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
Larger values of r2 imply that the observations are more closely grouped about the a. average value of the independent variables. b. average value of the dependent variable. c. least squares line. d. origin.
c
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
The level of significance, in hypothesis testing, is the probability of a. accepting a true null hypothesis. b. accepting a false null hypothesis. c. rejecting a true null hypothesis. d. rejecting a false null hypothesis.
c
The model developed from sample data that has the form of = b0 + b1x is known as the a. regression equation. b. correlation model. c. estimated regression equation. d. regression model.
c
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the a. correlation coefficient. b. standard error of the estimate. c. coefficient of determination. d. confidence interval estimate.
c
The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the a. chi-square distribution. b. normal distribution. c. F distribution. d. t distribution.
c
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. the probability distribution of the test statistic
c
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
In simple linear regression, r2 is the a. mean square error. b. correlation coefficient. c. squared residual. d. coefficient of determination.
d
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
The above equation implies that an a. increase of $1 in price is associated with a decrease of $8 in sales. b. increase of $8 in price is associated with a decrease of $52,000 in sales. c. increase of $1 in price is associated with a decrease of $52 in sales. d. increase of $1 in price is associated with a decrease of $8000 in sales.
d
The p-value a. can be any negative value. b. can be any positive value. c. must be a number between -1 and 0. d. must be a number between zero and one.
d
The p-value is a. the same as the z statistic. b. a sample statistic. c. a distance. d. a probability.
d
The power curve provides the probability of a. correctly accepting the null hypothesis. b. incorrectly accepting the null hypothesis. c. incorrectly rejecting the null hypothesis. d. correctly rejecting the null hypothesis.
d
The practice of concluding "do not reject H0" is preferred over "accept H0" when we a. are conducting a one-tailed test. b. are testing the validity of a claim. c. have an insufficient sample size. d. have not controlled for the Type II error.
d
The probability of committing a Type I error when the null hypothesis is true as an equality is a. the confidence level. b. β. c. greater than 1. d. the level of significance.
d
The random variable for a chi-square distribution may assume a. any value between -1 to 1. b. any value between -∞ to +∞. c. any negative value. d. any value greater than zero.
d
The standard error of the estimate is the a. standard deviation of t. b. square root of SSE. c. square root of SST. d. square root of MSE.
d
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
Which of the following has a chi-square distribution? a. (n - 1)σ2/s2. b. (n - 1)σ/s. c. (n - 1)s/σ. d. (n - 1)s2/σ2.
d
Which of the following has an F distribution? a. (n - 1)s/σ. b. s1/s2. c. (n - 1)s1/s2. d. .
d
f the coefficient of correlation is a positive value, then the a. intercept of the regression line must also be positive. b. coefficient of determination can be either a negative or a positive value, depending on the slope. c. regression equation could have either a positive or a negative slope. d. slope of the regression line must be positive.
d
