1) The statement that determines if the null hypothesis is rejected or not is called the
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2) What are the critical z-values for a two-tailed hypothesis test if the significant level = 0.01?
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3) A hypothesis test that involves a small sample requires that we make the following assumption that
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4) Doi Winery has two wine shops in the neighboring towns of Seamen and Batavia. The favorite wine, as advertised, is Raspberry wine. A survey of 300 customers at the Seamen store revealed that 225 individuals preferred the Raspberry wine while 290 out of 400 in Batavia preferred the same flavor. To test the hypothesis that there was no difference in preferences in the two towns, what is the alternate hypothesis?
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5) K & S Construction, located in Phoenix, Arizona, is working on its business plan for the upcoming year. They did a study to determine if they should focus on building condominiums or individual houses. A building study, which had been conducted by the state, indicated that 60 percent of those families looking to buy a home in Arizona desired to buy a condominium. K & S Construction wanted to know if this figure applied to Phoenix. They collected a sample of 500 individuals that had expressed plans to buy a new home. The z-distribution was selected for this proportion test. The null hypothesis is p = 0.60 and the alternate is p ≠ 0.60. The significant level selected was .05. From the sample of 500, it was determined that 290 wanted to buy a condominium. What decision should be made regarding the null hypothesis?
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6) In classical hypothesis testing, the test statistic is to the critical value what the ________________.
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7) When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are
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8) If the paired differences are normal in a test of mean differences, then the distribution used for testing is the
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9) You are conducting a two-tailed test of means but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is
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10) A recent study by College Stat Company reported a nationwide survey of college students determined that students spend 2 hours studying for each hour in the classroom. Professor Baker at State College wants to determine whether the time students spend at her college is significantly different from the national average of 2 hours. A random sample of 20 statistics students resulted in an average of 1.75 hours with a standard deviation of 0.24 hours. A t-test was conducted at the 5% level of significance. The calculated value of t was -4.03. What was Professor Baker decision?
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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
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12) Golf balls that are properly manufactured will have a rebound height of 42 inches when dropped by a testing machine from a height of 5 feet. The quality control inspector is concerned that a new manufacturing machine is not properly calibrated and that the resulting golf balls are falling short of the desired height. At random, 100 golf balls were selected for a test. The test results indicated that the rebound height was 41.6 inches with a standard deviation of 0.5. At the .05 significant level, what is the result of the test?
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13) The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test. He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis?
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14) Indy H2O is a water bottling company. They are looking at two different bottling manufacturers’ equipment for the purpose of replacing some old equipment. The net weights of a sample of bottles filled by a machine manufactured by WTR, and the net weights of a sample filled by a similar machine manufactured by Target are (in grams): WTR: 8, 9, 7, 8, 9, and 10 Target: 8, 10, 7, 11, 9, 12, 8, and 9 Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Target machine is greater than the mean weight of the bottles filled by the WTR machine, what is the critical value?
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15) When is it appropriate to use the paired difference t-test?
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16) What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on two samples, both sample sizes are 13?
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17) You are conducting a two-tailed test of means, but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is
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18) When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are
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19) New college business graduates are finding it difficult to get a job. A business journal has reported that only one in five graduates is able to find a job within 6 months of their graduation. A report by the University of Phoenix indicated that out of a survey of 300 recent business graduates, 75 had jobs. You are a business major at the University of Phoenix and have a concern about getting a job. Based on this data, will a graduate of the University of Phoenix have a better chance of getting a job in the first 6 months after graduation? Use the .05 significant level for the test.
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20) Watson’s TV claims that their televisions have the best performance record on the market. They advertise that after 3 years only 10% of their sold televisions have had any type of repairs. The president of the company wanted to confirm that this statement was correct. To do this, a sample of 60 sets was taken of sets that had been sold and were at least 3 years old. Twelve percent of these television sets had been in for repair. The null hypothesis is that there is no difference between the stated percent and the sample data. At the .05 significant level, what can we conclude about the null hypothesis?
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21) The accountant for Thomas’s Furniture Store is concerned regarding the outstanding receivable owed the company. There has been a cash flow problem and it is believed that the slow collection of accounts receivable is partially the blame. The accountant believes that 40% of the present accounts are more than 4 months behind in making payments. To be able to make a decision regarding this belief, a random sample of 100 accounts was taken. It was found that 37 accounts were more than 4 months late. Did the sample data confirm the accountant’s belief? Use the .05 significant level for the statistical test.
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22) Mr. Thomas owns three different restaurants in Cincinnati, Ohio. He is concerned about the profitability of the restaurants. There are monthly differences between the restaurants and he wants to determine if the differences in profit are significant. Mr. Thomas wants to do a statistical test to see if he should be concerned. The best test to address this problem would be
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23) Which is NOT a valid assumption for the utilization of the ANOVA test?
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24) In the metro area there are four major supermarket chains. To determine if there was a difference between these stores, regarding their pricing of food, a consumer group did a test. In the Eastgate area of town, each of the supermarket chains has a store. Twenty-five common household items were selected for the test. These items were purchased at each of the four stores and the prices were compared. To analyze this data, what would be the best statistical test to use?
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25) In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by
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26) If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?
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27) Each Christmas season there is a hot toy that everyone must have, especially if you are under the age of nine. This prized toy can be purchased at many different types of stores. A consumer group wanted to determine if there was a difference in price for the toy depending on where the toy was purchased. Is the price of this toy the same for the different stores or is there a difference? In the Cincinnati area there are three main stores of concern: Wal-Mart, Meijer, and Toys R Us. Data was collected from different stores around the city. Prices will vary depending on the location of the store. The collected data is as follows (in dollars):
Conduct an ANOVA analysis of the data. Is there a significant difference between the three stores?
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28) The chi-square has
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29) The chi-square distribution is
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30) What nonparametric test is used when the assumptions for the parametric analysis of variance (ANOVA) cannot be met? Its purpose is to test whether three or more populations are equal. The data must be at least ordinal scaled.
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31) The city of Denver has several golf courses around the city. The Recreational Park manager is trying to set the schedule for the employees at these courses. His concern is that he wants to have enough staff to handle the daily demands but to not be overstaffed. He has concerns about the next year’s budget and is trying to curb expenses where possible. To be able to make a decision regarding staffing, he collected data regarding the number of rounds of golf played during the week. The weekend was excluded because the weekends are always very busy. He wanted to see if there was a significant difference between the days of the week in terms of rounds being played. If there was a difference, then he could use this information to help make staffing decisions. The result of the data collection is as follows:
What is the result of the statistical test? Can the manager’s staff schedule vary for different days of the week? Use the chi square distribution at the .05 significant level.
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32) The reason the computed chi-square value is positive is because the difference between the observed and expected frequencies is
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33) Rachael Smith is the personnel manager at Johnson and Johnston, an accounting firm. She is concerned about tardiness, which seems to be an increasing problem, especially after days off work. She decided to sample the records to determine if tardiness was distributed evenly throughout the 6-day work week. The null hypothesis to be tested was: Tardiness is distributed evenly throughout the week. The 0.01 level was used as the significant level. The sample results were:
What is the critical value of chi-square with a significant level of = 0.05?
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34) To determine whether four population means are equal, a sample from each population was selected at random and using the Kruskal-Wallis test, H was computed to be 2.11. What is your decision at the 0.05 level of risk?
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35) The Big Toy House is a local company that specializes in selling children outdoor playhouses. With many businesses there is a certain amount of difficulty in collecting money on past due accounts. This has become a concern of the owner. A recent trade magazine indicated that the national averages for account receivable were: 65% current, 25% late, and 10% not collectable. A recent study of the company’s records indicated that 60 percent of the account receivable is current. Thirty percent of the accounts were late and the remaining 10% of receivable were viewed as being not collectable. To determine if his store was in-line with the national average, the manager had a statistical analysis performed. The chi square test was selected for the analysis and the .05 significant level was used. The test statistics was X² = 6.725. What is the correct decision regarding this result?
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36) Clermont Savings and Loan has four branches located throughout the county. The activity level at these four branches appears to be different but the manger needs verification. Turnover rate, how quickly money is withdrawn from an account after being deposited, was selected as the variable to be measured. A total sample of 22 accounts was collected from the four Branches. The Kruskal-Wallis test, at the .01 significant level, was selected for the statistical analysis. The null hypothesis being tested was that the population distribution between the four branches is identical. The test statistics was H = 12.453. What is the correct interpretation of this result?
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37) What does a coefficient of correlation of 0.70 infer?
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38) Based on the regression equation, we can
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39) A simple linear regression generated a correlation coefficient of 0.01. This tells us that
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40) The Ohio Electric Company is investigating electric consumption by single family homes based on the number of rooms. The investigators wanted to determine the relationship between number of rooms and electric consumption in kilowatt-hours (thousands). A sample of 12 homes was selected and the data is as follows:
What percent of the variation is explained by the variable, number of rooms?
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41) The Golden Park and Recreation Department wants to determine a better way to estimate income at the various recreational centers. One relationship that was investigated was between family size and amount spent on recreation. The question was if smaller families spent less money than larger families. A regression analysis tool was selected to be used to address this question. Data was collected from 15 member families regarding what they spent each week on recreation. Their data was as follows:
Compute the coefficient of correlation.
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42) Smith’s Appliances is evaluating its advertising budget. The owner is trying to decide if the budget needs to be altered or not. The question: Is there a positive return on the investment that is being made in advertising? What is the relationship between sales and the amount spent on advertising? The owner collected data for the past year by month. The data is in millions of dollars.
Is there a relationship between the two variables? What is the coefficient of correlation for this data?
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43) Thomas and Thomas, a large plumbing company in Louisville, has a huge staff of plumbers that are utilized on contractual projects. Before a plumber is hired, an aptitude test must be taken and passed. After a plumber is hired they are evaluated on their performance. Each plumber receives a job performance score based on their individual production. The production manager wants to determine if there is a relationship between the performance score and the aptitude test score. Additionally, the manager wanted to investigate the influence that being a union member has on performance (coded as 1 union member and 0 nonmembers). An analysis of 20 plumbers was conducted. The resulting equation was Performance = 28.1 + 4.85 Aptitude + 20.5 Union. What is your interpretation of this analysis?
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44) When an insurance company is going to write a new home owner policy, one concern is the distance between the house and the nearest fire department station. This is one factor that goes in to determining the cost of the insurance for the home owner. ETB Insurance Company wants to determine if there is a relationship between the distance to a fire station and the amount of fire damage to a house. A random sample of 50 claims was selected for analysis. The correlation coefficient was 0.78. Which is the correct interpretation and recommendation?
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45) The Actuarial Department of an insurance company was assigned the task of determining the relationship between the distance to a fire station and the amount of damage to a house. This is one factor that is utilized in determining the cost of insurance for a home owner. A sample of 35 claims was selected from last year. When the analysis was completed the following regression equation was the result. (X is the distance to a fire station and Y' is the amount of damage in thousands of dollars) Y' = 11.65 + 5.12X If a house was 10 miles from the fire station, what would be the best estimate of the cost of damages to the house?
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46) In a multiple regression ANOVA table, explained variation is represented by
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47) Which of the following statements about multiple regression is TRUE?
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48) If the net regression coefficients in the population are significantly different from zero, what can be included?
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49) If a quarterly seasonal index is 0.66, it implies that
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50) A time series is
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51) The time series component that reflects variability over short, repetitive time periods that last less than one year is called
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52) Midwest State University Office of Registrar is reviewing the university’s enrollment for the past 10 years. It is know that there are seasonal variable that affects the university’s enrollment. To be better able to address business decisions that are affected by enrollment, an analysis of data was necessary. The school operates on a quarter system of enrollment starting typically with fall quarter and ending with summer quarter. The analysis of the data produced these four quarterly indexes.
Which statement is correct based on this analysis?
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53) The owner of a local construction company that specializes in outdoor structures desires to make a prediction regarding the next business year sales. Expansion of the business is one possible decision that could be made. It has been determined that the business needs to be at least $8 million dollars in annual sales before expansion could be considered. The following is data for the past 6 years. (Sales in millions of dollars.)
The statistical analysis of the data produced this least square trend equation. Y' = 7.634 + 0.05457t What should the owner's decision be regarding expansion in 2010?
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54) An analysis of graduates from a local business college was performed to determine if there was a relationship between GPA and starting salary of recent graduates. It was believed that a higher GPA would result in a higher starting salary. The analysis of data collected from recent graduates produced the following correlation matrix.
Which statement is correct regarding the interpretation of the analysis?
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Exam – 2
1) Type II error is committed when we reject a null hypothesis that is true. A. True B. False
2) If the p-value is less than a in a two-tailed test, the null should be rejected. 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) In classical hypothesis testing, the test statistic is to the critical value what the ________________.
A. level of significance is to the test statistic
B. p-value is to alpha
C. critical value is to alpha
D. test statistic is to the p-value
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. (0.34-0.35)/0.063
B. (0.35-0.34)/100
C. (0.34-0.35)/0.015
D. (0.35-0.34)/0.2275
6) 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 appropriate set of hypotheses to determine if the Senatorial concern is valid?
A. H0: B ? 0.35 H1: B < 0.35
B. H0: B = 0.35 H1: = B > 0.35
C. H0: B # X.XX H1: = B > 0.34
D. H0: : # XX,XXX H1: : > 28,000
7) A test for equality of two variances is based on
A. the ratio of the sample variances
B. A. the difference between the sample variances.
C. the difference between the population variances.
D. C. the difference between the sample coefficients of variation.
8) You are conducting a two-tailed test of means but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is
A. need a table to calculate this value.
B. 0.13
C. 0.065
D. 0.26
9) A test for equality of two variances has samples sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are
A. 12 and 9.
B. 21.
C. 26.
D. 13 and 10.
10) In a test of the equality of two means, the variable of interest is the difference between the values of the observations, rather than the observations.
A. True B. False
11) The pooled variance of the two samples is the average of the sample variances when n1 = n2.
A. True B. False
12) Which of the following statements is false for an F-distribution?
A. Degrees of freedom for the numerator may be larger, smaller, or equal to the degrees of freedom for the denominator.
B. Variables that are F distributed range from 0 to infinity.
C. The exact shape of the distribution is determined by two numbers of degrees of freedom.
D. Degrees of freedom for the denominator are always smaller than degrees of freedom for the numerator.
13) Which of the following statements is consistent with the Central Limit Theorem?
A. Means of samples of n=30 from an exponential distribution will be approximately normally distributed.
B. When µ and s are known, the population will be approximately normally distributed.
C. If a population has µ and s, a sample from that population will be normally distributed if the sample size is large enough.
D. When we know s, the variation in the sample means will be equal to that of the population.
14) The standard error of the sample mean is equal to 5 when n=25. If the sample size increases by a factor of four, who will the standard error change?
A. It will double.
B. It will be cut to ¼ of 5.
C. It will be cut in half.
D. It will quadruple.
15) 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 size N>30.
C. When the population is symmetric.
D. For all populations.
16) When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are
A. normal with equal variances.
B. are non-normal and have equal variances.
C. are normal with unequal variances.
D. are non-normal and have unequal variances.
17) 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. samples are independently drawn from the populations.
C. sample sizes are small.
D. null hypothesis states that the two population proportions are equal.
18) A test for equality of two variances has sample sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are
A. 21.
B. 13 and 10.
C. 26.
D. 12 and 9.
19) 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
20) If we simultaneously examine the effects of two factors on the dependent variable, along with the effects of interactions between different levels of those factors, we are performing a three-factor analysis of variance.
A. True B. False
21) An analysis of variance (ANOVA) tests population variance.
A. True B. False
22) Hartley's test measures the equality of the means for several groups.
A. True B. False
23) When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.
A. True B. False
24) Comparison of c means in a one-factor ANOVA is the same as using c repeated t-tests.
A. True B. False
25) The appropriate measure of central location of ordinal data is the
A. mean.
B. median.
C. mode.
D. all of these.
26) Consider the following data set: 14, 14, 15, 16, 18, 19, 19, 20, 21, 22, 23, 25, 25, 25, 25, and 28. The rank assigned to the four observations of value 25 is
A. 12
B. 13
C. 12.5
D. 13.5
27) The nonparametric counterpart of the parametric one-way analysis of variance F-test is the
A. Kruskal-Wallis test.
B. Spearman’s rho.
C. Friedman test.
D. Wilcoxon signed rank sum test.
28) A test of independence in a contingency table with five rows and four columns has the following degrees of freedom:
A. 20
B. 9
C. 12
D. 7
29) Of the values for a chi-squared test statistic listed below, which one is most likely to lead to rejecting the null hypothesis in a goodness-of-fit test?
A. 45
B. 1.2
C. 2.1
D. 0
30) 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. alternative hypothesis is false, and we would reject it.
C. null hypothesis is true, and we would not reject it.
D. chi-squared distribution is invalid, and we would use the t-distribution. instead
31) How many runs are in the sequence TFTFFFFTTF?
A. 2
B. 5
C. 4
D. 6
32) If each group has at least five observations, the distribution of the Kruskal-Wallis H is
A. F
B. x2
C. t
D. z
33) The nonparametric counterpart of the randomized block model of the ANOVA is the
A. Wilcoxon rank sum test.
B. Wilcoxon signed rank sum test.
C. Kruskal-Wallis test.
D. Friedman test.
34) Two models were proposed for a simple regression of tree height on bark thickness, Model A: Height’ = 7.8*Bark + 37 and Model B: Height’ = 8*Bark + 35. Using the information and calculations below, which model is best? Model A: Height’ = 7.8*Bark + 37 Tree ID Height (feet) Bark Thickness (millimeters) Predicted Height Error Squared Error 1 150 15 2 175 18 177.4 -2.4 5.76 3 225 21 200.8 24.2 585.64 4 200 23 216.4 -16.4 268.96 Model 8: Height’ = 8*Bark + 35 Tree ID Height (feet) Bark Thickness (millimeters) Predicted Height Error Squared Error 1 150 15 155 -5 25 2 175 18 179 -4 16 3 225 21 203 22 484 4 200 23
A. Model A
B. Model B
C. The models are identical.
D. It is impossible to determine the best model.
35) 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. $123,000.
B. $487,500.
C. $4,875.
D. $12,300.
36) The least squares line is the line guaranteed to be the line of all possible lines
A. that has the smallest squared sum of the distance between observations and predictions.
B. that has the smallest sum of squared distance between observations and predictions.
C. around which the smallest square be drawn.
D. that connects the most observations with the fewest turns.
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) The least squares regression line is obtained when the sum of the squared residuals is minimized.
A. True B. False
39) 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
40) An inverse relationship between an independent variable x and a dependent variable y means that, as x increases, y decreases, and vice versa.
A. True B. False
41) 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
42) Except for the values r = -1, 0, and 1, we cannot be specific in our interpretation of the coefficient of correlation r. However, when we square it, we produce a more meaningful statistic.
A. True B. False
43) If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to
A. the absence of binary variables.
B. the presence of binary variables.
C. autocorrelation
D. multicollinearity.
44) Which of the following statements about multiple regression is TRUE?
A. If we have taken into account all relevant explanatory factors, the residuals from a multiple regression should be random.
B. The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares and subtracting that value from 1.
C. A multiple regression is called multiple because it has several data points.
D. The total sum of squares in a regression model will never exceed the regression sum of squares.
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) If we want to measure the seasonal variations on stock market performance by quarter, we would need
A. 2 indicator variables.
B. 1 indicator variables.
C. 4 indicator variables.
D. 3 indicator variables.
47) A time series is
A. a model that attempts to analyze the relationship between a dependent variable and one or more independent variables.
B. a model that attempts to forecast the future value of a variable.
C. a set of measurements on a variable collected at the same time or approximately the same period of time.
D. a set of measurements on a variable taken over some time period in chronological order.
48) Smoothing time series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the
A. seasonal component.
B. irregular variation component.
C. trend component.
D. cyclical component.
49) When a change has occurred in the mean of the process distribution, the result is referred to as
A. a cycle.
B. a trend.
C. a level shift.
D. instability
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 under control.
B. out of control when it is out of control.
C. under control when it is out of control.
D. out of control when it is under control.
