RES 342- FINAL EXAM 1

1) The statement that determines if the null hypothesis is rejected or not is called the

A. decision rule
B. critical value
C. test statistic
D. alternate hypothesis

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

A. ± 2.58
B. ± 1.65
C. ± 2.33
D. ± 1.96 3) An independent consumer testing lab preformed a statistical test on 25 type-C alkaline batteries and calculated the mean life for a particular use before they failed was 22.5 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.1 hours. Information on the package states that the batteries should last 24 hours. The test question was if this difference between the test statistics and the stated life of the battery was significant? The .05 significant level was selected for the test. Which is the correct statement? The article I selected is called “Selective immunoglobulin A deficiency in children with diabetes mellitus: Data from a medical center in Ukraine.” This article reports a study done in western Ukraine. The goal of the study was to estimate the prevalence of selective immunoglobulin A  deficiency (SIgAD) among children with type 1 diabetes mellitus (DM). (Selective IgA deficiency is an immune system condition in which you lack or don’t have enough immunoglobulin A (IgA), a protein that fights infection) (MayoClinic.org). According to this article, SIgAD is one of the most common primary immunodeficiencies, and its prevalence ranges from 1:300 to 1:3000 depending o the population.  SIgAD is diagnosed in children older than four years with serum IgA below 7mg/dL, with normal immunoglobulins G (IgG) and M(IgM) and other causes of hypogammaglobulinemia and T cells defects ruled out.  In addition, the article also reports that this deficiency is a heterogeneous condition with a multifactorial mechanism and its pathogenesis is not completely understood and typically is associated with defects in B cells failing to produce IgA and T cell abnormalities and cytokine abnormalities also may play a role on this deficiency. A. The difference cannot be evaluated with this small of a sample. B. The difference indicates that the batteries are not good. C. The difference was not significant. D. The difference was significant; the batteries do not meet the stated length of time.

4) 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. Cannot accept nor reject it based on the information given
B. The test level of .05 is not acceptable
C. Reject it
D. Fail to reject it

5) In classical hypothesis testing, the test statistic is to the critical value what the ________________.

A. test statistic is to the p-value
B. level of significance is to the test statistic
C. critical value is to alpha
D. p-value is to alpha

6) A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ‗. Which of the following would solve this problem?

A. Convince upper management to use a smaller p-value.
B. Convince upper management to reduce the level of significance of the test.
C. Convince upper management to use a larger sample.
D. Convince upper management to use a larger p-value.

7) 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.

8) A machine is set to fill the small size packages of Good and Better candies are packaged with 60 pieces of candies in each bag. Sampling results revealed: 3 bags of 61, 2 bags of 59, 1 bag of 58, and 2 bags of 62. How many degrees of freedom are there?

A. 9
B. 7
C. 1
D. 8

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. F distribution
C. Chi-Square
D. Student t distribution

10) 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?

A. There is no significant difference.
B. A larger test sample is needed.
C. There is a significant difference; the golf balls are defected.
D. A decision regarding a significant difference cannot be made.

11) 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.

12) 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(1-0.025, 13, 10).
C. =FINV(0.025, 12, 9).
D. =FINV(0.025, 13, 10).

13) When is it appropriate to use the paired difference t-test?

A. Two independent samples are compared
B. Two dependent samples are compared
C. Four samples are compared at once
D. Any two samples are compared

14) 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. Accept the null hypothesis; there is not a significant difference.
B. This is a two tail test and the critical value for the test is 1.96.
C. There is not enough data available to answer the question.
D. Reject the null hypothesis; there is a significant difference.

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) 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. 0.26.
B. You need a table to calculate this value.
C. 0.13.
D. 0.065.

17) A consumer researcher is testing the difference between two proportions at the 0.05 level of significance. The researcher was utilizing the z distribution for the test. If the computed test statistic z value was 1.12, what was the decision?

A. Take a larger sample.
B. Reserve judgment.
C. Reject the null hypothesis.
D. Do not reject the null hypothesis.

18) 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

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 null hypothesis is rejected and the difference is significant.
B. The difference is too close to be able to decide.
C. The sample is too small to be able to decide.
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. There is enough evidence; move forward with the project.
B. A decision cannot be made either yes or no.
C. There is not enough evidence to support the moving 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. No, there is not a significant difference.
B. The business journal information is incorrect.
C. Yes, there is a significant difference.
D. Cannot be predicted based on this data.

22) 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. A paired t-test
B. An ANOVA
C. Chi square test
D. Kruskal-Wallis test

23) Analysis of variance is used to

A. compare nominal data
B. simultaneously compare several population means
C. compare population proportion
D. compute t test

24) The F distribution is utilized with the ANOVA test. There are some basic assumptions associated with the distribution. Which of these assumptions is NOT valid?

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A. It is negatively skewed.
B. Its values cannot be negative.
C. There is a family of distributions.
D. It is a continuous distribution.

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25) If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?

A. A difference between at least one pair of population means
B. The variances are the same
C. Too many degrees of freedom
D. No difference between the population means

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) 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):

Wal-Mart	Meijer	Toys R Us
15	18	20
12	17	19
12	14	16
14	15	20
13	17	19

Conduct an ANOVA analysis of the data. Is there a significant difference between the three stores?

A. A t-test would have been a better test.
B. There is a significant difference between the three stores.
C. The sample needs to be larger to be able to answer the question.
D. There is not a significant difference between the three stores.

28) The chi-square distribution becomes more symmetrical as

A. degrees of freedom decrease
B. degrees of freedom increase
C. number of variables increase
D. the chi-square value increases

29) 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

30) In the chi-squared goodness-of-fit test, if the expected frequencies e_i and the observed frequencies f_i 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

31) 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

32) Seamen’s Manufacturing has five hundred employees at its plant. These employees are divided into three main groups: administration, clerical, and labor. The company is looking at making some changes to it retirement plan that is available for employees. There are three plans beginning considered. The 500 employees were surveyed regarding their preferences for the various retirement plans. The president is concerned if there is a relationship between the person position in the company and which retirement plan was preferred. Utilize the chi square distribution at the .05 significant level, and determine if there is a relationship between position in company and the retirement plan selected.

Position	Plan A	Plan B	Plan C
Labor	170	50	30
Clerical	30	110	30
Administration	20	20	40

 

A. The calculated test result of 7.94 is less than the critical value, so accept the null hypothesis.
B. The calculated test result of 7.94 is less than the critical value, so reject the null hypothesis.
C. The calculated test result of 7.94 is greater than the critical value, so accept the null hypothesis.
D. The calculated test result of 7.94 is greater than the critical value, so reject the null hypothesis.

33) The Ohio Department of Highways is in the process of selecting a new paint for highway use. Four different paint companies have been contact regarding this need and each of the companies has supplied paint for testing. Before deciding the winner of the new contract, a test was conducted to determine which paint was the best, in terms of how long it would last. The results of the test are as follows:

Category	Paint A	Paint B	Paint C	Paint D
Days	345	320	350	310

Each paint is expected to last 330 days. Is there a significant difference between these four paints? Use the chi square distribution at the .05 significant level to answer this question.

A. The test result is greater than the critical value, so there is a significant difference.
B. The test result is less than the critical value, so there is not a significant difference.
C. A decision cannot be made; more testing is required.
D. Paint B and D are significantly different then paints A and C.

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?

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

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) 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

37) A simple linear regression generated a correlation coefficient of 0.01. This tells us that

A. SSR is almost zero.
B. SSE is almost zero.
C. we shall reject the null at less than a 5% significance level.
D. the two variables barely relate to each other.

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 does a coefficient of correlation of 0.70 infer?

A. Coefficient of determination is 0.49
B. Almost no correlation because 0.70 is close to 1.0
C. 70% of the variation in one variable is explained by the other
D. Coefficient of non-determination is 0.30

40) A researcher was investigating the relationship between the variables grades in high school and grades in college. The investigator wanted to determine if a relationship existed and if so, to what extent. A regression analysis was perform on the data and the correlation value was r = .71. Based on this finding, which statement is correct?

A. The researcher was able to explain about 36 percent of the variation in the problem by this variable.
B. The researcher was able to explain about 71% of the variation in the problem by this variable.
C. The researcher was able to explain about 50 percent of the variation in the problem by this variable.
D. The researcher was able to explain about 80 percent of the variation in the problem by this variable.

41) 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:

Number of Rooms	Kilowatt-Hours	Number of Rooms	Kilowatt-Hours
10	10	8	9
9	8	10	11
7	6	10	9
12	13	8	9
8	7	6	7
11	12	5	6

What percent of the variation is explained by the variable, number of rooms?

A. .901
B. .812
C. .451
D. .949

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.

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

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) 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?

A. There is not a strong enough relationship so as to be able to use distance to a firehouse as a factor in determining insurance rates.
B. The strong inverse relationship indicates that distance to a fire station is a reliable variable to consider as a factor in determining insurance rates.
C. The strong relationship indicates that distance to a fire station is a reasonable factor to be considered when determining insurance rates.
D. The variable, distance to a fire station, is able to explain 78% of the variation in the problem and so it is a reasonable factor to use in determining insurance rates.

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?

A. There is a direct relationship but it is weak.
B. For every mile that the house is from the fire station, there is an 11.65 increase in cost.
C. For every mile that the house is from the fire station, the damages to the house will increase by the factor 5.12.
D. The damages to a house that is 10 miles from a fire station would be about $53,000.

46) 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

47) In a multiple regression ANOVA table, explained variation is represented by

A. the regression sum of squares
B. the total sum of squares
C. the correlation matrix
D. the regression coefficients

48) 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

49) If the least squares equation for Mary’s Clothing sales data from 2004 to 2008 is represented by the equation Y‘ = 12 + 1.1t (in $ millions). What is the value of t and the forecast for 2010?

A. t = 10, y = 0.0
B. t = 6, y = 18.6
C. t = 1, y = 12.0
D. t = 7, y = 19.7

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

A. irregular variation.
B. long-term trend.
C. cyclical variation.
D. seasonal variation.

51) Given the trend equation Y‘ = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010?

A. 32
B. 25
C. 27
D. 31

52) 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.)

Year	Sales	Year	Sales
2004	7.45	2007	7.94
2005	7.83	2008	7.76
2006	8.07	2009	7.90

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?

A. Expansion decision could go either way based on data
B. Cannot make a decision based on this data
C. Expansion should be considered
D. Expansion should be delayed

53) 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.

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.