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that means if the null...

1) If a hypothesis test has a level of significance of 5%, that means if the null is true, we don’t reject it 5% of the time.

A. True

B. False

2) “µ = 17” is an appropriate null hypothesis.

A. True

B. False

3) The value that separates a rejection region from a non-rejection region is called the test statistic.

A. True

B. False

4) We have created a 95% confidence interval for µ with the result [10, 15]. What conclusion will we make if we test H0: µ = 16 versus H1: µ ? 16 at a = 0.05?

A. Accept the null.

B. Reject the null and conclude the alternative.

C. We cannot tell what our decisions will be from the information.

D. Fail to reject the null.

5) The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians. What is the test statistic for this hypothesis test?

A. (0.35-0.34)/100

B. (0.35-0.34)/0.2275

C. (0.34-0.35)/0.063

D. (0.34-0.35)/0.015

6) You performed a right-tailed hypothesis test and your sample gave you a test statistic in the left tail. Which of the following is considered the appropriate next step in this test?

A. Fail to reject the null.

B. Change the level of significance of your test.

C. Change the sample and do the test again.

D. Change the direction of the hypothesis.

7) A test for equality of two variances has samples sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are

A. 21.

B. 26.

C. 12 and 9.

D. 13 and 10.

8) A test for equality of two variances is based on

A. A. the difference between the sample variances.

B. the difference between the population variances.

C. the ratio of the sample variances

D. C. the difference between the sample coefficients of variation.

9) If the paired differences are normal in a test of mean differences, then the distribution used for testing is the

A. normal distribution

B. Chi-Square

C. F distribution

D. Student t distribution

10) Testing the difference of means of independent samples must always be a two-tailed test.

A. True

B. False

11) In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is

A. =FINV(0.05, 12, 9).

B. =FINV(0.025, 12, 9).

C. =FINV(1-0.025, 13, 10).

D. =FINV(0.025, 13, 10).

12) 100 women were polled and 60 reported successfully communicating an automobile problem to an auto repairman. A sample of 150 men had 95 reporting the same success. The value of the test statistic for a test of the equality of proportions is

A. -0.5319.

B. 0.7293.

C. 0.2702.

D. -0.419.

13) The expected value of the sampling distribution of the sample mean equals the populations mean

A. When the population is normally distributed.

B. When the population is symmetric.

C. When the population size N>30.

D. For all populations.

14) Which of the following statements is consistent with the Central Limit Theorem?

A. When µ and s are known, the population will be approximately normally distributed.

B. If a population has µ and s, a sample from that population will be normally distributed if the sample size is large enough.

C. When we know s, the variation in the sample means will be equal to that of the population.

D. Means of samples of n=30 from an exponential distribution will be approximately normally distributed.

15) A random variable follows the Student’s t distribution. The probability that it will be positive is

A. 1

B. .50

C. Less than 0.50

D. 0

16) A test for equality of two variances is based on

A. the difference between the sample variances.

B. the difference between the population variances.

C. the difference between the sample coefficients of variation.

D. the ratio of the sample variances.

17) If the paired differences are normal in a test of mean differences, the distribution used for testing is the

A. normal distribution.

B. chi-square.

C. student t distribution.

D. f distribution.

18) A pooled proportion estimate may be used to calculate the test statistic for a test of the equality of proportions when the

A. populations are normally distributed.

B. sample sizes are small.

C. samples are independently drawn from the populations.

D. null hypothesis states that the two population proportions are equal.

19) An analysis of variance (ANOVA) tests population variance.

A. True

B. False

20) The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.

A. True

B. False

21) The F-test of the randomized block design of the analysis of variance has the same requirements as the independent sample design; that is, the random variable must be normally distributed and the population variances must be equal.

A. True

B. False

22) Which of the following is not required to perform a one-factor ANOVA?

A. The sample sizes must be equal.

B. The samples for each treatment must be selected randomly and independently.

C. The populations must be normally distributed.

D. The population variances must be equal.

23) Hartley's test measures the equality of the means for several groups.

A. True

B. False

24) Which of the following statistics from the ANOVA table do not have an additive relationship?

A. Sum of squares

B. It is not possible to tell.

C. Degrees of freedom

D. Mean squares

25) The nonparametric counterpart of the parametric one-way analysis of variance F-test is the

A. Kruskal-Wallis test.

B. Wilcoxon signed rank sum test.

C. Friedman test.

D. Spearman’s rho.

26) The appropriate measure of central location of ordinal data is the

A. mean.

B. median.

C. mode.

D. all of these.

27) Statistical methods that require few assumptions, if any, about the population distribution are known as

A. nonparametric techniques.

B. All of these

C. parametric techniques.

D. free agent techniques.

28) In the chi-squared goodness-of-fit test, if the expected frequencies ei and the observed frequencies fi were quite different, we would conclude that the

A. null hypothesis is false, and we would reject it.

B. chi-squared distribution is invalid, and we would use the t-distribution. instead

C. null hypothesis is true, and we would not reject it.

D. alternative hypothesis is false, and we would reject it.

29) If each observation can be classified into one of several mutually exclusive and collectively exhaustive categories, the population is a

A. normal

B. chi-squared.

C. binomial.

D. multinomial.

30) The number of degrees of freedom in testing for normality is the

A. number of intervals used to test the hypothesis minus 1.

B. number of intervals used to test the hypothesis minus number of parameters estimated minus 1.

C. number of intervals used to test the hypothesis minus number of parameters estimated minus 2.

D. number of parameters estimated minus 1.

31) The Kruskal-Wallis test statistic may be approximated by a chi-squared distribution with c-1 degrees of freedom, where c is the number of populations, whenever the sample sizes are all greater than or equal to

A. 5

B. 25

C. 30

D. 15

32) For applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is:

A. All c population medians are the same.

B. At least two population medians are the same.

C. At least two population medians are different.

D. All c population medians are different.

33) How many runs are in the sequence TFTFFFFTTF?

A. 2

B. 5

C. 6

D. 4

34) A regression analysis between sales, in $1,000, and advertising, in $100, resulted in the following least squares line: Sales' = 75 + 6*(Advertising). This implies that if advertising is $800, sales will be

A. $4,875.

B. $12,300.

C. $123,000.

D. $487,500.

35) In regression analysis, if the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.

A. True

B. False

36) The value of the sum of squares for regression SSR can never be larger than the value of total sum of squares SST.

A. True

B. False

37) What randomness exists in the linear regression model?

A. The randomness from the explanatory variables, the X's

B. The randomness from what is unexplained, the error

C. The randomness of the dependent variable, the Y's

D. None of these

38) When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense.

A. True

B. False

39) When using the least squares method, the column of residuals always sums to zero.

A. True

B. False

40) If the coefficient of correlation is –0.81, then the percentage of the variation in y that is explained by the regression line is 81%.

A. True

B. False

41) Given that SSE = 84 and SSR = 358.12, the coefficient of correlation, also called the Pearson coefficient of correlation, must be 0.90.

A. True

B. False

42) The regression line y = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The sum of squares for error will be 10.0

A. True

B. False

43) Interpret the coefficient on gender.

A. Ceteris paribus: a male is paid $9,290 less on average than a female.

B. Ceteris paribus: a female is paid $9,290 less on average than a male.

C. Ceteris paribus: if a woman changes her gender, she will receive $9,290 less.

D. Ceteris paribus: for each additional dollar of salary, a female’s salary moves 9.29 units closer to a male’s salary.

44) If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

A. Independence of errors

B. Normality of the errors

C. Homoscedasticity

D. None of these

45) If the Durbin-Watson statistic, DW, has values greater than 2, this indicates

A. a positive first–order autocorrelation.

B. a negative first–order autocorrelation.

C. no first–order autocorrelation at all.

D. None of the above

46) For which of the following values of the smoothing constant a will the smoothed series catch up most quickly whenever the original time series changes direction?

A. 0.90

B. 0.50

C. 0.40

D. 0.10

47) If we want to measure the seasonal variations on stock market performance by quarter, we would need

A. 4 indicator variables.

B. 3 indicator variables.

C. 2 indicator variables.

D. 1 indicator variables.

48) The time series component that reflects variability over short, repetitive time periods that last less than one year is called

A. long–term trend.

B. cyclical variation.

C. seasonal variation.

D. irregular variation.

49) When the only sources of variation in a production process are caused by chance, the process is said to be

A. out of balance but under control.

B. out of control but in balance.

C. under control.

D. out of control.

50) Variations in process output that are caused by a number of randomly occurring events that are part of the production process are

A. special causes.

B. common causes.

C. out-of-control causes.

D. All of the these

51) In statistical process control, a Type I error occurs if we decide that the process is

A. under control when it is out of control.

B. out of control when it is under control.

C. under control when it is under control.

D. out of control when it is out of control.

A. True

B. False

2) “µ = 17” is an appropriate null hypothesis.

A. True

B. False

3) The value that separates a rejection region from a non-rejection region is called the test statistic.

A. True

B. False

4) We have created a 95% confidence interval for µ with the result [10, 15]. What conclusion will we make if we test H0: µ = 16 versus H1: µ ? 16 at a = 0.05?

A. Accept the null.

B. Reject the null and conclude the alternative.

C. We cannot tell what our decisions will be from the information.

D. Fail to reject the null.

5) The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians. What is the test statistic for this hypothesis test?

A. (0.35-0.34)/100

B. (0.35-0.34)/0.2275

C. (0.34-0.35)/0.063

D. (0.34-0.35)/0.015

6) You performed a right-tailed hypothesis test and your sample gave you a test statistic in the left tail. Which of the following is considered the appropriate next step in this test?

A. Fail to reject the null.

B. Change the level of significance of your test.

C. Change the sample and do the test again.

D. Change the direction of the hypothesis.

7) A test for equality of two variances has samples sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are

A. 21.

B. 26.

C. 12 and 9.

D. 13 and 10.

8) A test for equality of two variances is based on

A. A. the difference between the sample variances.

B. the difference between the population variances.

C. the ratio of the sample variances

D. C. the difference between the sample coefficients of variation.

9) If the paired differences are normal in a test of mean differences, then the distribution used for testing is the

A. normal distribution

B. Chi-Square

C. F distribution

D. Student t distribution

10) Testing the difference of means of independent samples must always be a two-tailed test.

A. True

B. False

11) In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is

A. =FINV(0.05, 12, 9).

B. =FINV(0.025, 12, 9).

C. =FINV(1-0.025, 13, 10).

D. =FINV(0.025, 13, 10).

12) 100 women were polled and 60 reported successfully communicating an automobile problem to an auto repairman. A sample of 150 men had 95 reporting the same success. The value of the test statistic for a test of the equality of proportions is

A. -0.5319.

B. 0.7293.

C. 0.2702.

D. -0.419.

13) The expected value of the sampling distribution of the sample mean equals the populations mean

A. When the population is normally distributed.

B. When the population is symmetric.

C. When the population size N>30.

D. For all populations.

14) Which of the following statements is consistent with the Central Limit Theorem?

A. When µ and s are known, the population will be approximately normally distributed.

B. If a population has µ and s, a sample from that population will be normally distributed if the sample size is large enough.

C. When we know s, the variation in the sample means will be equal to that of the population.

D. Means of samples of n=30 from an exponential distribution will be approximately normally distributed.

15) A random variable follows the Student’s t distribution. The probability that it will be positive is

A. 1

B. .50

C. Less than 0.50

D. 0

16) A test for equality of two variances is based on

A. the difference between the sample variances.

B. the difference between the population variances.

C. the difference between the sample coefficients of variation.

D. the ratio of the sample variances.

17) If the paired differences are normal in a test of mean differences, the distribution used for testing is the

A. normal distribution.

B. chi-square.

C. student t distribution.

D. f distribution.

18) A pooled proportion estimate may be used to calculate the test statistic for a test of the equality of proportions when the

A. populations are normally distributed.

B. sample sizes are small.

C. samples are independently drawn from the populations.

D. null hypothesis states that the two population proportions are equal.

19) An analysis of variance (ANOVA) tests population variance.

A. True

B. False

20) The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.

A. True

B. False

21) The F-test of the randomized block design of the analysis of variance has the same requirements as the independent sample design; that is, the random variable must be normally distributed and the population variances must be equal.

A. True

B. False

22) Which of the following is not required to perform a one-factor ANOVA?

A. The sample sizes must be equal.

B. The samples for each treatment must be selected randomly and independently.

C. The populations must be normally distributed.

D. The population variances must be equal.

23) Hartley's test measures the equality of the means for several groups.

A. True

B. False

24) Which of the following statistics from the ANOVA table do not have an additive relationship?

A. Sum of squares

B. It is not possible to tell.

C. Degrees of freedom

D. Mean squares

25) The nonparametric counterpart of the parametric one-way analysis of variance F-test is the

A. Kruskal-Wallis test.

B. Wilcoxon signed rank sum test.

C. Friedman test.

D. Spearman’s rho.

26) The appropriate measure of central location of ordinal data is the

A. mean.

B. median.

C. mode.

D. all of these.

27) Statistical methods that require few assumptions, if any, about the population distribution are known as

A. nonparametric techniques.

B. All of these

C. parametric techniques.

D. free agent techniques.

28) In the chi-squared goodness-of-fit test, if the expected frequencies ei and the observed frequencies fi were quite different, we would conclude that the

A. null hypothesis is false, and we would reject it.

B. chi-squared distribution is invalid, and we would use the t-distribution. instead

C. null hypothesis is true, and we would not reject it.

D. alternative hypothesis is false, and we would reject it.

29) If each observation can be classified into one of several mutually exclusive and collectively exhaustive categories, the population is a

A. normal

B. chi-squared.

C. binomial.

D. multinomial.

30) The number of degrees of freedom in testing for normality is the

A. number of intervals used to test the hypothesis minus 1.

B. number of intervals used to test the hypothesis minus number of parameters estimated minus 1.

C. number of intervals used to test the hypothesis minus number of parameters estimated minus 2.

D. number of parameters estimated minus 1.

31) The Kruskal-Wallis test statistic may be approximated by a chi-squared distribution with c-1 degrees of freedom, where c is the number of populations, whenever the sample sizes are all greater than or equal to

A. 5

B. 25

C. 30

D. 15

32) For applications of the Kruskal-Wallis test, the alternative hypothesis to be tested is:

A. All c population medians are the same.

B. At least two population medians are the same.

C. At least two population medians are different.

D. All c population medians are different.

33) How many runs are in the sequence TFTFFFFTTF?

A. 2

B. 5

C. 6

D. 4

34) A regression analysis between sales, in $1,000, and advertising, in $100, resulted in the following least squares line: Sales' = 75 + 6*(Advertising). This implies that if advertising is $800, sales will be

A. $4,875.

B. $12,300.

C. $123,000.

D. $487,500.

35) In regression analysis, if the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.

A. True

B. False

36) The value of the sum of squares for regression SSR can never be larger than the value of total sum of squares SST.

A. True

B. False

37) What randomness exists in the linear regression model?

A. The randomness from the explanatory variables, the X's

B. The randomness from what is unexplained, the error

C. The randomness of the dependent variable, the Y's

D. None of these

38) When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense.

A. True

B. False

39) When using the least squares method, the column of residuals always sums to zero.

A. True

B. False

40) If the coefficient of correlation is –0.81, then the percentage of the variation in y that is explained by the regression line is 81%.

A. True

B. False

41) Given that SSE = 84 and SSR = 358.12, the coefficient of correlation, also called the Pearson coefficient of correlation, must be 0.90.

A. True

B. False

42) The regression line y = 2 + 3x has been fitted to the data points (4,11), (2,7), and (1,5). The sum of squares for error will be 10.0

A. True

B. False

43) Interpret the coefficient on gender.

A. Ceteris paribus: a male is paid $9,290 less on average than a female.

B. Ceteris paribus: a female is paid $9,290 less on average than a male.

C. Ceteris paribus: if a woman changes her gender, she will receive $9,290 less.

D. Ceteris paribus: for each additional dollar of salary, a female’s salary moves 9.29 units closer to a male’s salary.

44) If the Durbin-Watson statistic has a value close to 0, which assumption is violated?

A. Independence of errors

B. Normality of the errors

C. Homoscedasticity

D. None of these

45) If the Durbin-Watson statistic, DW, has values greater than 2, this indicates

A. a positive first–order autocorrelation.

B. a negative first–order autocorrelation.

C. no first–order autocorrelation at all.

D. None of the above

46) For which of the following values of the smoothing constant a will the smoothed series catch up most quickly whenever the original time series changes direction?

A. 0.90

B. 0.50

C. 0.40

D. 0.10

47) If we want to measure the seasonal variations on stock market performance by quarter, we would need

A. 4 indicator variables.

B. 3 indicator variables.

C. 2 indicator variables.

D. 1 indicator variables.

48) The time series component that reflects variability over short, repetitive time periods that last less than one year is called

A. long–term trend.

B. cyclical variation.

C. seasonal variation.

D. irregular variation.

49) When the only sources of variation in a production process are caused by chance, the process is said to be

A. out of balance but under control.

B. out of control but in balance.

C. under control.

D. out of control.

50) Variations in process output that are caused by a number of randomly occurring events that are part of the production process are

A. special causes.

B. common causes.

C. out-of-control causes.

D. All of the these

51) In statistical process control, a Type I error occurs if we decide that the process is

A. under control when it is out of control.

B. out of control when it is under control.

C. under control when it is under control.

D. out of control when it is out of control.

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Mr. Gregory White

Master's Degree

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JACUSTOMER-yrynbdjl-

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I have taught college Mathematics for the past 10 years.

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Dr Arthur Rubin

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BA Maths, Oxford

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