# RES 342 FINAL EXAAM 4

## RES 342 FINAL EXAAM 4

RES 342 FINAL EXAAM 4

1. A hypothesis test that involves a small sample requires that we make the following assumption that

A. the confidence interval will be wider than for large samples

B. the region of acceptance will be wider than for large samples

C. a larger computed value of t will be needed to reject the null hypothesis

D. the population is normally distributed

2. What are the critical z-values for a two-tailed hypothesis test if the significant level = 0.01?

A. ± 1.65

B. ± 1.96

C. ± 2.58

D. ± 2.33

3. What is the critical value for a two-tail, one sample hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 23?

A. 1.717

B. 2.074

C. 2.069

D. 1.714

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?

A. µ1 = µ2

B. µ1 < µ2 C. µ1 ≠ µ2 D. µ1 > µ2

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?

A. The test level of .05 is not acceptable

B. Fail to reject it

C. Cannot accept nor reject it based on the information given

D. Reject it

6. 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

7. Cake manufacturer Little Diva’s wants to increase the shelf life of its easy-to-fix cupcake mixes. Company’s records indicate that the average shelf life of the mix is 230 days. A new, improved cupcake mix was developed and a sample of 10 boxes of the cupcake mix had these shelf lives (in days): 231, 233, 232, 233, 228, 231, 234, 229, 235, and 232. If the standard deviation was .67 and at the 0.025 significant level, has the shelf life of the cupcake mix increased?

A. No, because computed t lies in the region of acceptance.

B. Yes, because computed t is greater than the critical value.

C. No, because 231.8 is quite close to 230.

D. Yes, because computed t is less than the critical value

8. Thomas Delivery has a fleet of 24 trucks that are utilized for the companies; business. Electro-Lite, a manufacturer of spark plugs, claims that its spark plugs have an average life in excess of 25,000 miles. The purchasing agent at Thomas Delivery purchased 24 sets and found that the sample average life was 26,300 miles, the sample standard deviation was 1,500 miles, and the computed test statistic was t = 3.423. Based on these findings, at the 0.05 level, is there enough evidence to accept the manufacturer’s claim?

A. Electro-Lite claims are not supported by the test results.

B. Electro-Lite claims are supported; the spark plugs do exceed the mean of 25,000 miles.

C. Electro-Lite claims cannot be supported or denied with the test results.

D. Electro-Lite claims are just an advertising promotion.

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

A. f distribution.

B. chi-square.

C. student t distribution.

D. normal distribution.

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?

A. Cannot make a decision at this time; more data is required.

B. Reject the alternative hypothesis statement.

C. Fail to reject the null hypothesis.

D. Reject the null hypothesis, the test statistic exceeds the critical value

11. One hundred 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. -0.419.

C. 0.7293.

D. 0.2702

12. Newton’s, a tire manufacturer, wanted to set a mileage guarantee on its new Road Warrior 60 tire. A sample test of 500 tires revealed that the tire’s mileage is normally distributed with a mean of 50,000 miles and a standard deviation of 1,750 miles. The warranty on the tires is presently set at 47,500 miles. The z-test statistic result was 1.43. The manufacturer wanted to determine if the tires were exceeding the guarantee. At the .05 significant level, it was concluded that the tires are exceeding the manufacturer’s guarantee.

A. The evidence does not support this decision.

B. This was the correct decision.

C. The decision needs to be delay until more data is collected.

D. A decision cannot be made.

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?

A. This is a two tail test and the critical value for the test is 1.96.

B. Accept the null hypothesis; there is not a significant difference.

C. Reject the null hypothesis; there is a significant difference.

D. There is not enough data available to answer the question.

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 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?

A. 2.179

B. 1.761

C. 2.145

D. 1.782

15. Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?

Product FIFO (F) LIFO (L)

1 225 221

2 119 100

3 100 113

4 212 200

5 248 245

The 5% level of significance was selected for the t value. This example is what type of test?

A. Paired t-test.

B. Test of proportions.

C. One sample test of means.

D. Two sample test of means

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?

A. 1.708

B. 2.064

C. 2.060

D. 1.711

17. When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are

A. are normal with unequal variances.

B. are non-normal and have equal variances.

C. normal with equal variances.

D. are non-normal and have unequal variances.

18. Two different accounting procedures that are utilized by businesses as a way to evaluate their inventory are LIFO (Last In First Out) and FIFO (First In First Out). ABC manufacturer evaluated its finished goods inventory (in $ thousands) for five products using both procedures. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?

Product FIFO (F) LIFO (L)

1 225 221

2 119 100

3 100 113

4 212 200

5 248 245

The 5% level of significance was selected for the t value. The calculated test statistic was 1.93. What is the decision?

A. Fail to reject the null hypothesis and conclude LIFO is not more effective.

B. Reject the alternate hypothesis and conclude LIFO is more effective.

C. Fail to reject the null hypothesis and conclude LIFO is more effective.

D. Reject the null hypothesis and conclude LIFO is more effective.

19. 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?

A. The difference is too close to be able to decide.

B. The sample is too small to be able to decide.

C. The null hypothesis is rejected and the difference is significant.

D. The data fails to reject the null hypothesis.

20. A trolley system is being planned for the downtown area of Cincinnati, Ohio. To be able to proceed with this project, planners have indicated that at least 20% of the residents of the areas that would be covered need to support the idea. To determine the feelings of these city residents, a sample of 300 residents was taken. Seventeen percent of the sample responded that they would ride the trolley. Is this enough evidence for the project to proceed? Use the .05 level of significant.

A. A decision cannot be made either yes or no.

B. There is not enough evidence to support the moving forward with the project.

C. There is enough evidence; move forward with the project.

D. A t-test would be the best choice for the test.

21. 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.

A. The business journal information is incorrect.

B. Yes, there is a significant difference.

C. No, there is not a significant difference.

D. Cannot be predicted based on this data.

22. Analysis of variance is used to

A. compare nominal data

B. simultaneously compare several population means

C. compare population proportion

D. compute t test

23. Blake’s Mortgage Company utilizes four different appraisers for the purpose of determining the value of a house. There is a concern by the company’s owner that the appraisers are not providing the same estimates. She wants to determine if there is a difference between the four appraisers. Six houses were selected and each appraiser provided an appraisal for each of the six houses. What would be the best statistical test to use for the analysis of this data?

A. An ANOVA

B. Chi square test

C. A paired t-test

D. Kruskal-Wallis test

24. 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

A. to conduct a two sample test

B. to conduct an ANOVA test

C. to conduct a paired t-test

D. to conduct two different t tests

25. Ace Car Rental has three main models that are used in it midsize range of cars. The cars are very similar and perform at about the same level. Since the customer has to pay for the gas use during the rental period, the manager is often asked about which car gets the best gas mileage. To be able to address this question, an analysis was done of the three makes of cars. Each car can use any one of four different grades of gasoline. The data collected was for each car for each type of fuel. Performance was measured in miles per gallon. Perform an ANOVA test and state the results.

Gasoline Model A Model B Model C

Regular 21.4 22.3 20.8

Super Regular 20.6 17.1 19.5

Unleaded 21.3 19.2 20.2

Premium 20.5 20.3 18.5

A. F = 6.54, there is a significant difference between models.

B. F = 2.41, there is not a significant difference between models.

C. F = 5.67, there is a significant difference between models.

D. F = 1.39, there is not a significant difference between models.

26. In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by

A. doing an additional ANOVA

B. doing a t test

C. constructing confidence intervals

D. adding another treatment

27. Robinson, a large department store, wanted to example to look at which credit cards were being utilized for purchases. A sample of 18 credit card sales was taken and recorded. The amounts charged for each of three different credit cards, MasterCard, Visa, and Discover, were: six MasterCard sales, seven Visa sales, and five Discover sales. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic?

A. 6 in the numerator, 15 in the denominator

B. 2 in the numerator, 15 in the denominator

C. 18 in the numerator, 3 in the denominator

D. 3 in the numerator, 18 in the denominator

28. 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.

A. Mann-Whitney

B. ANOVA

C. Students’ t

D. Kruskal-Wallis

29. 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 [ID: 29826]

A. alternative 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 false, and we would reject it

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

30. The chi-square has

A. a family of distributions

B. a uniform distribution

C. one distribution

D. two distributions

31. The reason the computed chi-square value is positive is because the difference between the observed and expected frequencies is

A. always positive

B. squared

C. uniform

D. linear

32. The nonparametric counterpart of the randomized block model of the ANOVA is the

A. Wilcoxon signed rank sum test

B. Wilcoxon rank sum test

C. Kruskal-Wallis test

D. Friedman test

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:

Day of Week Number Absent

Monday 12

Tuesday 9

Wednesday 11

Thursday 10

Friday 9

Saturday 9

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What is the critical value of chi-square with a significant level of = 0.05?

A. 12.592

B. 15.033

C. 13.388

D. 11.070

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34. Corny’s Feed Company markets four different mixtures of feed for chickens. These feeds have different combinations of ingredients. One question that the manager is often asked by customers is if there is a difference between the four feeds in terms of weight gain. To be able to address this question an analysis was done of the four feeds. They contacted a local farmer to conduct a test regarding the four feeds. There were 28 chickens selected for the test. These chickens were divided into four groups, with each group receiving one of the feeds. The statistical test selected for the analysis was the Kruskal-Wallis test and the .05 significant level was used for the test. The test result was H 4.65. This indicates that

A. the feeds are different

B. the feeds need to be tested some more before a decision can be made

C. the feeds are the same

D. some of the feeds are different

35. State Insurance Company believes that the age of the driver and number of accidents that occurs are related. The feeling is that younger drivers are more careless and will have more accidents. The claims department wants to determine if this line of thinking is correct. To answer this question a random sample of 1500 policyholders was investigated. A chi square analysis was performed on the data at the .05 significant level. The analysis produced a chi square value of 47.56. What is the correct decision regarding the null hypothesis that whether a claim is filed and the age of the policyholder are not related?

A. The sample needs to be larger; no decision can be made.

B. Reject the null hypothesis; there is a relationship.

C. The null hypothesis is incorrect.

D. Accept the null hypothesis; there is no relationship.

36. 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?

A. Fail to reject the null hypothesis because 0.05 < 2.11 B. Fail to reject the null hypothesis because 2.11 < 7.815 C. Reject the null hypothesis because 2.11 > critical value of 1.96

D. Reject the null hypothesis because 7.815 is > 2.11

37. Based on the regression equation, we can

A. predict the value slope of the line

B. predict the value of the dependent variable given a value of the independent variable

C. measure the association between two variables

D. predict the value of the independent variable given a value of the dependent variable

38. What is the variable used to predict another variable called?

A. Independent variable

B. Dependent variable

C. Causal variable

D. Important variable

39. What is the range of values for a coefficient of correlation?

A. –1.0 to +1.0 inclusive

B. 0 to +1.0

C. Unlimited range

D. –3 to +3 inclusive

40. 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.

Month Advertising Expense Sales Revenue

January 2 4

February 3 5

March 3 6

April 5 8

May 6 8

June 4 7

July 5 7

August 6 8

September 7 9

October 8 10

November 10 13

December 9 11

Is there a relationship between the two variables? What is the coefficient of correlation for this data?

A. Yes, 0.961

B. Yes, 0.892

C. Yes, 0.980

D. No, 0.457

41. 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

42. 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:

Family Size Amount Spent Family Size Amount Spent Family Size Amount Spent

4 $109 3 101 3 115

5 114 4 120 6 174

3 161 4 125 5 156

5 159 6 170 4 145

5 164 3 104 5 145

Compute the coefficient of correlation.

A. .463

B. .861

C. .618

D. .681

43. The least squares regression equation is Y’ = 1312 + 245X. When X = 5, what does Y’ equal?

A. 2357

B. 1557

C. 4,050

D. 2537

44. In the least squares equation, Y’ = 12 + 25X the value of 25 indicates

A. for each unit increase in X, Y increases by 25

B. the Y intercept

C. for each unit increase in Y, X increases by 25

D. the X factor

45. If the coefficient of correlation is 0.69, the coefficient of determination is

A. 0.8306

B. 0.4401

C. 0.6898

D. 0.4761

46. If there are four independent variables in a multiple regression equation, there are also four

A. Y-intercepts

B. regression coefficients

C. constant terms

D. dependent variables

47. Conducting a multiple regression analysis, the residual analysis is used to test the requirement that

A. the independent variables are the direct cause of the dependent variable

B. the number of independent variables included in the analysis is correct

C. the variation in the residuals is the same for all fitted values of Y`

D. prediction error is minimized

48. If the net regression coefficients in the population are significantly different from zero, what can be included?

A. At least one of the net regression coefficients is not equal to zero.

B. Good predictions are not possible.

C. No relationship exists between the dependent variable and any of the independent variables.

D. Very strong correlations exist among the variables.

49. If a quarterly seasonal index is 0.66, it implies that

A. the other three quarter percentages will total 34%

B. the quarter’s sales are 66% of the yearly average

C. the quarter’s sales are 66% of the year total sales

D. the quarter’s sales are 6% above the yearly average

50. The following linear trend equation was developed for the annual sales of the Tractor Manufacturing Company. Y’ = 355 + 50t (in $ thousands). How much are sales increasing by?

A. $50,000 per year

B. $5,000 per month

C. $6,000 per year

D. $500,000 per year

51. 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.

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.

Fall Winter Spring Summer

1.2617 1.1896 1.1040 0.4447

Which statement is correct based on this analysis?

A. Winter and spring quarters should be treated differently.

B. Summer quarter appears to be too low.

C. Fall quarter needs to receive major attention to handle enrollment.

D. The pattern is predictable and reasonable.

53. With the increased cost in fuel, there has been a shift in the buying habits of new car purchasers. A local car dealer was interested in determining if there was a significant difference in fuel efficiencies between three sizes of car: compact, midsize and large. The manager did a random sample of 27 cars. An ANOVA was used as the analysis tool using a significant level of .01. The results of the ANOVA were as follows:

Source of Variation SS df MS F p-value

Between Groups 130.44 2 65.22 7.97 0.0017

Within Groups 196.24 24 8.18

Total 326.68 36

The manger’s decision would be

A. the mean fuel efficiency of the car cannot be compared

B. to reject the null hypothesis; there is a significant difference between cars

C. to accept the null hypothesis; there is not a significant difference between cars

D. this was not the correct test for this data; a series of student t tests would have been better

54. Big House Lumber Company, located in Dayton, Ohio, is preparing its annual business report. The manager has performed an analysis of the business annual sales starting in 2004 and concluding with 2009. This analysis produced an annual sales linear trend equation of Y’ = 10.0989 + 0.14213t. The manager has been indicating to the company’s investors that sales in 2011 will exceed $11.5 million dollars. Is the manager statement accurate?

A. The manager has interpreted the data correctly.

B. The manager is providing the investors with a good prediction.

C. The manager is overstating the annual sales.

D. The manager is in need of more information before making a prediction.