RES 342 FINAL EXAAM 3


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RES 342 FINAL EXAAM 3

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1. If the decision is to reject the null hypothesis of no difference between two population parameters, z distribution at the .01 significant level, what is the correct statement of the alternate hypothesis and rejection region?
A. 2: z > 1.96 and z< negative 1.96
B.1 > 2; z< negative 2.33
C.1 2 ; z> 2.58 and z < negative 2.58
D.1 > 2 ; a> 2.33


2. the area of rejection, on a bell shaped curve, defines the location of all those values that are
A. so small or so large that the probability of their occurrence under a false null hypothesis is rather remote
B. so small or so large that the probability of their occurrence under a true null hypothesis is to be expected
C. Within the selected confidence interval for the test
D. So small or so large that the probability of their occurrence under a true null hypothesis is rather slim.

3. A hypothesis test that involves a small sample requires that we make the following assumption that
A. The region of acceptance will be wider than for large samples
B. The confidence interval 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 in normally distributed

4.In classical hypothesis testing, the test statistic is to the critical value what the ________________.
A. critical value is to alpha
B. test statistic is to the p-value
C. p-value is to alpha
D.level of significance is to the test statistic

5.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

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 test statistic for this hypothesis test?
A. (0.34-0.35)/0.015
B. (0.35-0.34)/100
C. (0.35-0.34)/0.2275
D. (0.34-0.35)/0.063

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

8) 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. Yes, because computed t is less than the critical value
B. Yes, because computed t is greater than the critical value
C. No, because computed t lies in the region of acceptance
D. No, because 231.8 is quite close to 230

9) 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 cannot be supported or denied with the test results.
B. Electro-Lite claims are not supported by the test results.
C. Electro-Lite claims are just an advertising promotion
D. Electro-Lite claims are supported; the spark plugs do exceed the mean of 25,000 miles.

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

11) Flash Jolt, a manufacturer of camera equipment, annually introduces new models in the fall of the year. At the conclusion of the Christmas season, retail dealers are contacted regarding their stock on hand of each piece of equipment. It has been discovered that unless 47% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. At the end of the 2009 Christmas shopping season a survey of 100 dealers indicated that 45% of Flash Jolt equipment had been sold. It was decided to continue production levels at the current levels. The statistical test was conducted at the 0.05 level. Computed z = –0.40.
A. Correct decision, not a significant difference
B. The two percentage points be attributed to sampling error
C. Wrong decision, should have cut back production
D. Cannot determine based on information given

12) 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. Fail to reject the null hypothesis.
B. Reject the alternative hypothesis statement.
C. Cannot make a decision at this time; more data is required.
D. Reject the null hypothesis, the test statistic exceeds the critical value



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

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?
A. 2.145
B. 1.761
C. 2.179
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. Two sample test of means
B. Test of proportions
C. One sample test of means
D. Paired t-test


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


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) If the paired differences are normal in a test of mean differences, the distribution used for testing is the
A. chi-square
B. student t distribution
C. normal distribution
D. f distribution


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 data fails to reject the null hypothesis.
B. The sample is too small to be able to decide.
C. The null hypothesis is rejected and the difference is significant
D. The difference is too close to be able to decide.

20) 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.
A. The accountant belief is not conferred.
B. The accountant belief is conferred.
C. There is not enough evidence to confer or deny the belief
D. The accountant needed to take a larger sample.


21) 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 t-test would be the best choice for the test.
C. A decision cannot be made either yes or no.
D. There is not enough evidence to support the moving forward with the project

22) 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?
A. It is negatively skewed.
B. It is a continuous distribution.
C. Its values cannot be negative.
D. There is a family of distributions


23) Which is NOT a valid assumption for the utilization of the ANOVA test?
A. The samples are independent.
B. The populations have equal standard deviations.
C. The samples are from populations that follow the normal distribution
D. The MSE/MST provides the test statistics for the F distribution

24) 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. Kruskal-Wallis test
C. An ANOVA
D. Chi square test


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 = 5.67, there is a significant difference between models.
B. F = 1.39, there is not a significant difference between models
C. F = 6.54, there is a significant difference between models.
D. F = 2.41, there is not a significant difference between models


26) Totto, an automobile manufacturer, has designed a radically new engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon were recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel are the same?
A. 1.96
B.12.00
C.2.33
D.4.07

27) If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate?
A. too many degrees of freedom
B. the variances are the same
C. a difference between at least one pair of population means
No difference between the population means

28) 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. 0
C. 1.2
D. 2.1


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. null hypothesis is false, and we would reject it
B. chi-squared distribution is invalid, and we would use the t-distribution instead
C. alternative hypothesis is false, and we would reject it
D. null hypothesis is true, and we would not reject it

30) The chi-square distribution is
A. positively skewed
B. negatively or positively skewed
C. normally distributed
D. negatively skewed

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:
Day of Week Rounds
Monday 150
Tuesday 90
Wednesday 120
Thursday 100
Friday 140
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.
A. Yes, there is a significant difference between days of the week.
B. No, there is a significant difference between days of the week.
C. No, there is not a significant difference between days of the week.
D. Yes, there is no difference between days of the week.

32) 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. Paint B and D are significantly different then paints A and C.
C. A decision cannot be made; more testing is required.
D. The test result is less than the critical value, so there is not a significant difference.
33) 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 greater 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 less than the critical value, so reject the null hypothesis.
34) What is your decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 7.815 and the computed value is 6.789?
A. The difference is probably due to sampling error; do not reject the null hypothesis.
B. Not due to chance; do not reject the alternate hypothesis.
C. Too close; reserve judgment.
D. Not due to chance; reject the null hypothesis.
35) 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. some of the feeds are different
C. the feeds are the same
D. the feeds need to be tested some more before a decision can be made
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?
A. The null hypothesis is accepted.
B. A different test needs to be used for the analysis.
C. More information is needed to be able to make a decision.
D. The null hypothesis is rejected



37) Correlation coefficients of positive 0.88 and negative 0.88 represent relationships between two variables that have
A. strong positive relationships
B. equal strength inverse relationships
C. equal weak relationships
D. equal strength but different directions
38) A simple linear regression generated a correlation coefficient of 0.01. This tells us that
A. SSR is almost zero.
B. the two variables barely relate to each other.
C. we shall reject the null at less than a 5% significance level.
D. SSE is almost zero.
39) If the coefficient of multiple determination is 0.72, what percent of variation is not explained?
A. 28%
B. 85%
C. 52%
D. 71%
40) 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. None of these
D. The randomness of the dependent variable, the Y's
41) 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 71% of the variation in the problem by this variable.
B. The researcher was able to explain about 50 percent of the variation in the problem by this variable.
C. The researcher was able to explain about 80 percent of the variation in the problem by this variable.
D. The researcher was able to explain about 36 percent of the variation in the problem by this variable.
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) 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?
A. These variables are not a good predictor of performance.
B. Being a union member increases the typical performance by 20.5.
C. The aptitude test is not a significant variable in this equation and needs to be eliminated as a variable.
D. The company would be wise to discourage union membership.
44) In the least squares equation, Y' = 12 + 25X the value of 25 indicates
A. the Y intercept
B. for each unit increase in X, Y increases by 25
C. the X factor
D. for each unit increase in Y, X increases by 25
45) 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
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) Multiple regression analysis assumes or requires that
A. the dependent variable is measured using an ordinal, interval, or ratio scale
B. the residuals follow an F-distribution
C. the observations are auto-correlated
D. the independent variables and the dependent variable have a linear relationship
48) 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 variation in the residuals is the same for all fitted values of Y`
C. the number of independent variables included in the analysis is correct
D. prediction error is minimized


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 = 6, y = 18.6
B. t = 10, y = 0.0
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. long–term trend.
B. irregular variation.
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. 25
B. 32
C. 27
D. 31
52) 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 is providing the investors with a good prediction.
B. The manager has interpreted the data correctly.
C. The manager is overstating the annual sales.
D. The manager is in need of more information before making a prediction.
53)
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.
Salary GPA
0.902
Business 0.911 0.851
Which statement is correct regarding the interpretation of the analysis?
A. The belief that there is a relationship between GPA and starting salary is correct.
B. GPA is explaining about 50% of the variation.
C. The belief that there is a relationship between GPA and starting salary is incorrect.
D. Nothing can be stated based on this data analysis.
54)
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. to accept the null hypothesis; there is not a significant difference between cars
B. this was not the correct test for this data; a series of student t tests would have been better
C. to reject the null hypothesis; there is a significant difference between cars
D. the mean fuel efficiency of the car cannot be compared

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