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1) In a two-sample test of means for independent samples, the equal sign always appears in

a. The null hypothesis.

b. The alternate hypothesis.

c. The upper tail of the test statistic.

d. None of the above.

2) In a two-sample test of means for independent samples, we use the z distribution when

a. The population standard deviations are equal.

b. Both populations have at least 4000 observations.

c. Both population standard deviations are known.

d. nB and n(1-B) are both greater than 5.

3) Which of the following is a requirement for a two-sample test of proportions.

a. The population standard deviations are equal.

b. Both populations are positively skewed.

c. Both samples are at least 30.

d. nB and n(1-B) are both greater than 5.

4) A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the degrees of freedom are

a. 18

b. 17

c. 16

d. None of the above

5) A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the critical value(s) are

a. 2.552

b. -2.921, 2.921

c. -2.583, 2.583

d. None of the above

6) Which of the following is not a requirement for the two-sample test of means for independent samples observations?

a. Normal populations

b. Equal population standard deviations

c. Equal sample sizes

d. All of the above are required.

7) To conduct a test of means for two independent samples which of the following are always required?

a. At least one of the samples must have 30 observations.

b. Both samples must have 30 observations.

c. np and n (1 - p) must be 5.

d. None of the above.

8) To conduct a test of hypothesis for dependent samples we assume that

a. The distribution of the difference between the paired observations follows the normal distribution.

b. Both samples are at least 30.

c. The samples are unrelated.

d. All of the above.

9) When conducting a test of hypothesis for the dependent samples

a. We should have at least 30 pairs.

b. The significance level is more than .05.

c. The p-value is more than .10.

d. None of the above

10) Which of the following is not necessary to determine a 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. All of the above.

11) The term ANOVA

a. Has no special meaning.

b. Stands for Analysis of Variance.

c. Stands for Another Numerical Observation of the Variance.

d. None of the above.

12) The general idea of analysis of variance is to compare estimates of variance

a. From both between the treatment means and within the treatment means

b. Based on the several treatments.

c. From within the treatments.

d. None of the above.

13) Which of the following is not a characteristic of the F distribution?

a. It is a discrete distribution.

b. In cannot be negative.

c. It is based on two sets of degrees of freedom.

d. All of the above.

14) The term “Treatment” refers to

a. A source of variation.

b. The numerator degrees of freedom.

c. The variation within the cells.

d. None of the above.

15) Suppose we select 6 observations from each of three treatments. The appropriate degrees of freedom are

a. 3 and 6.

b. 2 and 6.

c. 2 and 15.

d. None of the above

16): The term MSE

a. Is called the mean square error.

b. Is found by SSE/(n - k).

c. Is an estimate of the common population variance.

d. All of the above.

17) Which of the following is not an assumption required for ANOVA?

a. The populations are normally distributed

b. The populations have equal standard deviations

c. The samples are independent.

d. All of the above.

18) Under which of the following conditions will the computed value of F be negative?

a. When there is no difference in the treatment means

b. When there is no difference in the block means

c. When the SS total is larger than SST.

d. F cannot be negative.

19) Suppose we conduct an ANOVA test of four treatment means and reject the null hypothesis. Construction of a confidence interval for the difference between the first and second sample mean revealed the interval to be 10 plus or minus 12. We conclude

a. This pair of means differ.

b. This pair of means does not differ.

c. Because we do not know the units involved, we cannot draw any conclusion.

d. Because we do not know the degrees of freedom, we cannot draw any conclusion.

20) In a two-way ANOVA the second source of variation is due to

a. Random error.

b. Blocks.

c. Total variation

d. None of the above

21) A scatter diagram is a chart

a. In which the dependent variable is scaled along the vertical axis.

b. In which the independent variable is scaled along the horizontal axis.

c. That portrays the relationship between two variables.

d. All of the above.

22) In correlation analysis

a. We consider several independent variables.

b. We study the strength of the association between two variables.

c. We consider the intercept with the Y-axis.

d. None of the above.

23) The sample coefficient of correlation

a. Has the same sign as the slope, i.e. b.

b. Can range from -1.00 up to 1.00

c. Is also called Pearson=s r.

d. All of the above.

24) The coefficient of determination

a. Is the square of the coefficient of correlation.

b. Cannot be negative.

c. Reports the percent of the variation in the dependent variable explained by the independent variable.

d. All of the above.

25) Suppose we developed the following least squares regression equation: Y= = 3.5 + 2.1X. Which of the following statements are correct?

a. The dependent variable increases 2.1 for an increase of 1 in X.

b. The equation crosses the Y-axis at 3.5.

c. If X = 5, then Y= = 14.

d. All of the above.

26) The standard error of estimate is

a. Based on squared deviations from the regression line.

b. May assume negative values.

c. Is in squared units of the independent variable.

d. All of the above.

27) Which of the following is not a necessary condition for regression analysis.

a. The standard deviation of each of the conditional distributions must be the same.

b. The Y values are independent.

c. For each X value, there is a group of Y values and these Y values are normally distributed.

d. The slope of the regression line is positive (increasing).

28) Which of the following is not based on squared deviations from the regression line?

a. The coefficient of correlation.

b. The coefficient of determination.

c. The standard deviation.

d. The standard error of estimate.

29) In an ANOVA table for regression, the degrees of freedom for regression is

a. Equal to 1.

b. n - 1.

c. n - 2.

d. None of the above.

30) The term SSR/SS total is also called the

a. Sum of squares due to regression.

b. Coefficient of determination.

c. Standard error of estimate.

d. Coefficient of correlation.

QNT 561- 5

1) In a multiple regression equation there

a. Are two or more independent variables.

b. Is only one dependent variable.

c. Is one intercept value.

d. All of the above.

2) A dummy variable or indicator variable

a. May assume only a value of 0 or 1.

b. Is another term for the dependent variable.

c. Is found by (Y - ?).

d. Is equal to ?

3) The multiple standard error of estimate is

a. Is based on the (Y – Y)2.

b. Is negative when one of the net regression coefficients is 0.

c. Is found by taking the square root of SSR/SS total.

d. All of the above.

4) In the ANOVA table the value of k is

a. The number of independent variables.

b. The total number of observations

c. The number of degrees of freedom.

d. The sum of squares total.

5) A correlation matrix

a. Shows all simple coefficients of correlation.

b. Shows all possible net regression coefficients.

c. Shows the correlations that are positive.

d. Reports the multiple regression equation.

6) In a multiple regression equation

a. There is only one dependent variable.

b. The R2 term must be at least .50.

c. All the regression coefficient must be between -1.00 and 1.00.

d. None of the above.

7) Multicollinearity occurs when

a. The residuals are correlated.

b. Time is involved in the analysis

c. The independent variables are correlated.

d. The residuals are not constant for all Y' values.

8) In a global test of hypothesis we determine

a. Which independent variables do not equal 0.

b. Whether any of the set of independent variables differ from 0.

c. Whether any of the correlation coefficients differ from 0.

d. None of the above.

9) In testing the significance of individual regression coefficients

a. The test statistic is the t distribution.

b. We test the independent variables individually.

c. We usually delete the variables where the null hypothesis is not rejected.

d. All of the above.

10) The residual

a. Is the difference between the actual and the predicted value of the dependent variable.

b. Cannot assume a negative value.

c. Is also called the correlation matrix.

d. Has the same degrees of freedom as the MSE term.

11) To conduct a nonparametric test the

a. Population must follow the normal distribution.

b. The standard deviation must be known.

c. It is not necessary to make any assumption about the shape of the population.

d. The data must be at least interval scale.

12) Which of the following is not a characteristic of the X2

a. Its shape is based on the sample size.

b. It is not negative.

c. It is positively skewed.

d. It approaches a normal distribution as the degrees of freedom increase.

13) In a goodness-of-fit test where the sample size is 200, there are 5 categories, and the significance level is .05. The critical value of X2 is

a. 9.488

b. 11.070

c. 43.773

d. None of the above.

14) In a goodness-of-fit test

a. All the cell frequencies must be the same.

b. There must be at least 30 observations.

c. Forty percent of the cells must contain at least 10 observations.

d. None of the above.

15) In a contingency table

a. The number of rows must be the same as the number of columns.

b. A variable is classified according to two criteria.

c. There must be at least 10 observations in each cell.

d. All of the above.

16) In a contingency table a sample of 400 people is classified by gender and hair color (4 groups: blond, brown, black, and red). How many degrees of freedom are there?

a. 3

b. 8

c. 399

d. None of the above.

17) For a X2 goodness-of-fit test

a. There is only one degree of freedom.

b. The rejection region is in the upper right tail.

c. The scale of measurement is interval.

d. We must assume a normal population.

18) To find the expected frequency in a contingency table

a. Take the square root of the degrees of freedom.

b. Multiple the row total by the column total and divide the result by the grand total.

c. Use the total number of observations minus one.

d. None of these.

19) Suppose we select a sample of 100 observations and organize them into 6 categories. We wish to investigate whether the number of observations could be the same in each of the categories in the population. How many degrees of freedom are there?

a. 5

b. 97

c. 3

d. None of these.

20) Under what conditions could the X2 distribution assume negative values?

a. When the sample size is small.

b. When the cell frequencies are all equal.

c. When the degrees of freedom is 1.

d. Never

21) The philosophy of statistical quality control is to

a. Inspect the quality into the product.

b. Make it correct the first time.

c. Develop an adversarial relationship with the production department.

d. Shift costs from the manufacturing to the inspection department.

22) Dr. W. Edwards Deming

a. Was the founder of control charts.

b. Was an early craftsman in American industry.

c. Developed the ideas of acceptance sampling.

d. Helped Japan develop an overall plan to retool their production after World War II.

23) Chance variation is

a. Random in nature.

b. Can be completely eliminated from the process.

c. Is usually the result of a faulty production setup.

d. Is the basis of the Deming philosophy.

24) A Pareto Chart

a. Was developed by Dr. Walter A. Shewhart of the Bell Laboratories in the 1920s.

b. Is designed to show that 80 percent of the activity is caused by 20 percent of the factors.

c. Is one of Deming?s 14 points.

d. Highlights chance variation.

25) Which of the following is an example of a variable control chart?

a. An X- bar chart for means.

b. A percent defective chart.

c. A c- bar chart.

d. All of the above.

26) The Kimble Glass Company developed a control chart for the outside diameter of a syringe. Beginning at 7 AM this morning hourly checks showed the mean outside to diameter to be within the chart limits. Suddenly, the 2 PM check was above the UCL.

a. This is likely a random occurrence and production should be maintained.

b. This indicates that production is out of control. An adjustment should be made immediately.

c. This means that an error has been made in the calculation of the control limits.

d. This is an example of one of Deming?s 14 points.

27) The A2 factor is

a. Based on a constant relationship between the range and the standard deviation.

b. Used for variable charts.

c. Based on the size of the sample.

d. All of the above.

28) A c-bar chart shows the

a. Change in the mean.

b. Change in the range.

c. Number of defects per unit.

d. Percent defective.

29) The percent defective chart is

a. An example of a variable control chart.

b. A chart that shows the number of defects per unit.

c. A chart that shows the variation in weight of the unit produced.

d. An example of an attribute control chart.

30) In acceptance sampling the c value indicates the

a. Number of units sampled.

b. Probability of acceptance.

c. Number of defects per unit.

d. Allowable number of defects.

QNT-561 Set-6

QNT 561 Final Exam.

T F Q1: The number of individuals in a family is a continuous variable.

T F Q2: T-distributions are spread out more than a normal distribution with MU = 0, SIGMA = 1.

T F Q3: A random sample of 64 cars passing a check point on a certain highway showed a mean speed of 60 mph. The standard deviation of speeds is known to be 15 mph. In this case 60 mph is a point estimate of the population mean speed on this highway.

T F Q4: According to the Central Limit Theorem, the shape of the sampling distribution of sample mean (given that n ≥ 30) will be normal, whether or not the shape of the population is normal.

T F Q5: If the sample size is large (n ≥ 30), the standard deviation of the sample mean will equal the population standard deviation for that random variable.

T F Q6: Level of confidence is another name for level of significance.

T F Q7: If we would reject a null hypothesis at the 5% level, we would also reject it at the 1% level.

T F Q8: A Type I error is committed when one accepts the null hypothesis when it is false.

T F Q9: In a one-way ANOVA, when the null hypothesis is false, the calculated F-ratio would exceed the critical value of F for the chosen significance level.

T F Q10: Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.

T F Q11: Most nonparametric tests assume ordinal data.

T F Q12: One of the assumptions of regression analysis is that the error terms are normally distributed.

MULTIPLE CHOICE: Select the correct answer in each of Questions 11 to 25. There is only one correct answer to each question.

Q13: What area under the standard normal curve falls outside the Z values -1.96 and 1.96?

a. 0.05

b. 0.01

c. 0.90

d. 0.10

Q14: If each of a set of raw scores is transformed into a Z-score, the new distribution will have a standard deviation equal to

a. zero.

b. one.

c. the mean of the original distribution.

d. the standard deviation of the original distribution.

Q15: Which of the following random variables are continuous and which are discrete?

1. Score in a IQ Test

2. number of kittens in a litter

3. number of cars crossing a Traffic Light in one hour

4. the number of rainy days in a month

a. 1, 2 continuous; 3, 4 discrete

b. 1, 3, 4 continuous; 2 discrete

c. 4 continuous; 1, 2, 3 discrete

d. 1 continuous; 2, 3, 4 discrete

Q16: A factor that is varied by an experimenter in order to assess its effect is known as a(n):

a. dependent variable

b. independent variable

c. control variable

d. none of the above

Q17: For students' distribution, 90 percent of the area lies between t = -1.895 and t = 1.895 if the degrees of freedom are:

a. 6

b. 3

c. 7

d. 8

Q18: When (for what level of confidence) do we use Z = 1.645, for a two-sided test or confidence interval?

a. 90%

b. 95%

c. 80%

d. 100%

Q19: In finding confidence intervals for the mean of a normal population by using a t-statistic, student A uses a confidence coefficient of 0.95 while student B uses 0.99. Which one of the following statements is true about the length of the confidence intervals found by A and B?

a. B's interval will always be smaller than A's interval

b. B's interval will usually be smaller than A's interval

c. B's interval will always be larger than A's interval

d. B's interval will usually be larger than A's interval

Q20: We know the mean MU of a population. Suppose 1,000 samples of size n are drawn from this population. For each sample we compute a 90% confidence interval for MU. We would expect the mean of the population would NOT be contained within approximately how many of these intervals?

a. 0

b. 10

c. 100

d. 900

Q21: If the P-value for your test statistic satisfies p > .25, then:

a. you would not reject H(O) for ALPHA = .05

b. you would reject H(O) for ALPHA = .05

c. you would reject H(O) for ALPHA = .10

d. you would reject H(O) for ALPHA = .01

Q22:The appropriate alternative hypothesis for a lower tail test to determine if mean body weight of all the men who have joined a health club is less than 185 pounds would be

a. HA: μ ≥ 185 lb.

b. HA: μ < 185 lb.

c. HA: μ = 185 lb.

d. HA: μ ≠ 185 lb.

Q23: The e-mail usage for two different plants of a large company was compared at level of significance 0.05. A sample of 100 employees was selected at each plant. The mean number of e-mail messages sent per employee for one plant was 16 per week and the standard deviation was 4. For the other plant, the mean was 15 and the standard deviation was 3. For the test of equal population means versus unequal population means, the absolute value for the computed test statistic, the critical values, and the p-value respectively are:

a. 2, ± 1.96, 0.0455

b. 3, ± 2.33, 0.0027

c. 3, ± 1.96, 0.0455

d. 2, ± 1.65, 0.0455

Q24: Three samples of 10 were used to compare 3 population means. If the Sum of Squares Treatment (SST) is 350, what is the value for the Mean Square Treatment (MST)?

a. 350

b. 175

c. 35

d. 13

Q25: Which nonparametric test is analogous to a parametric two-sample t-test for means?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q26: Which nonparametric test is analogous to a parametric t-test for differences in paired data?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q27: Which nonparametric test is analogous to a one-factor ANOVA?

a. Wald-Wolfowitz test

b. Wilcoxon signed rank test

c. Mann-Whitney test

d. Kruskal-Wallis test

Q28: A linear regression between Y and X produced the following equation for the least squares line:

= -4.3 + 2.1x

Which of the following statements concerning this relationship is true?

a. For every one-unit increase in X, Y increases 4.3 units.

b. For every one-unit increase in X, Y decreases 2.1 units.

c. For every one-unit increase in X, Y decreases 4.3 units.

d. For every one-unit increase in X, Y increases 2.1 units.

Q29: The difference between an observed value of the dependent variable and its predicted value obtained from the regression equation is called a(n)

a. extrapolation.

b. interpolation.

c. residual.

d. mean deviation.

Q30: A regression line has been found and the statistician wants to know if the line has a slope. What is the appropriate null hypothesis to test?

a. H0: β1 = 0.

b. H0: β1 > 0.

c. H0: β1 < 0.

d. H0: β1 ≠ 0.

Solution Description

QNT 561 Set 4,5