RES 342 Final Exam ( A+ Solution )

 

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

A. ± 1.96

B. ± 2.33

C. ± 2.58

D. ± 1.65

2) In classical hypothesis testing, the test statistic is to the critical value what the __________.

A. ‘p-value’ is to alpha

B. critical value is to alpha

C. test statistic is to the ‘p-value’

D. level of significance is to the test statistic

 

3) For a hypothesis test of a single population mean at 95% confidence level, a calculated Z score of 1.7 supports the conclusion that

A. the population mean is greater than the hypothesized value

B. the null hypothesis cannot be rejected

C. the sample is biased

D. the population mean is less than expected

 

4) If the paired differences are normal in a test of mean differences, then the distribution used for testing is the

A. normal distribution

B. chi-square

C. student distribution

D. F distribution

 

5) 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. 0.7293

C. -0.419

D. 0.2702

 

6) Weekly sales of iPods® at 20 Best Buy® stores are compared before and after installing a new eye-catching display. To determine if the display is effective in increasing sales, what type of statistical test would you perform?

A. Comparison of means using independent samples using a t-test

B. Comparison of proportions using independent samples using a z-test

C. Comparison of means using a paired z-test

D. Comparison of means using a paired t-test

 

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

A. Four samples are compared at once.

B. Any two samples are compared.

C. Two independent samples are compared.

D. Two dependent samples are compared.

8) A survey of hotels found that the average hotel room rate in New Orleans is $88.42 and the average room rate in Phoenix is $80.61. The survey sampled 50 hotels in each city. The standard deviations were $5.62 and $4.83, respectively. At alpha=.05, it can be concluded that there is a significant different in the rates?

A. 7.45

B. -1.96

C. 1.96

D. -7.45

 

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

A. normal distribution

B. chi-square

C. student t distribution

D. F distribution

 

10) 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. There is not enough evidence to confirm or deny the belief.

B. The accountant’s belief is not confirmed.

C. The accountant’s belief is confirmed.

D. The accountant needed to take a larger sample.

 

11) 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 University of Phoenix indicated that out of a survey of 300 recent business graduates, 75 had jobs. You are a business major at University of Phoenix and have a concern about getting a job. Based on this data, will a graduate of 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. It cannot be predicted based on this data.

C. Yes, there is a significant difference.

D. The business journal information is incorrect.

 

12) Analysis of variance (ANOVA) is used to

A. compare nominal data

B. compute t- test

C. compare population proportion

D. simultaneously compare several population means

 

13) 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. a paired t- test

B. two different t tests

C. an ANOVA test

D. a two sample test

 

14) Sound engineers studied factors that might affect the output, in decibels, of a rock concert’s speaker system. The desired level of significance was a = .05. The results of their ANOVA tests are shown:  

Source of Variation                 SS                    df                    MS                  F                      P-value

Amplifier                     99.02344                                             99.02344                                             0.005718

Position                       93.98698                                             31.32899                     3.215807                     0.051003

Interaction                   10.15365                     3                      3.384549                     0.347412                     0.791505

Error                155.875                       16                    9.742188                                            

Total                359.0391                     23                                                                   

The interaction between the Position and Amplifier treatments was 

A. very significant

B. slightly significant

C. insignificant

D. highly correlated

 

15) 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 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. 4.07

C. 2.33

D. 12.00

 

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

A. Too many degrees of freedom

B. A difference between at least one pair of population means

C. No difference between the population means

D. The variances are the same

 

17) Nonparametric statistics are used when

A. you have qualitative data, with your variables being measured at the nominal or interval level

B. you have qualitative data, with your variables being measured at the ordinal or ratio level

C. you have qualitative data, with your variables being measured at the nominal or ordinal level

D. you have qualitative data, with your variables being measured at the ordinal or interval level

18) The nonparametric test most commonly used for testing the statistical independence between two variables is

A. the Kruskal- Wallis test

B. the Chi- Square test

C. the Mann Whitney test

D. the Sign test

 

19) What nonparametric test is used when the assumptions for the parametric 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. Students’ t

B. Kruskal- Wallis

C. Mann-Whitney

D. ANOVA

 

20) Rachael Smith is the personnel manager at Johnson and Johnston, an accounting firm. She is concerned about absenteeism, which seems to be an increasing problem, especially after days off work. She decided to sample the records to determine if absenteeism was distributed evenly throughout the 6-day work week. The null hypothesis to be tested was: Absenteeism is distributed evenly throughout the week. The sample results were:

 

Day of Week               Number Absent

Monday                       12

Tuesday                       9

Wednesday                 11

Thursday                     10

Friday              9

Saturday                      9

 

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

 

A. 11.070

B. 12.592

C. 13.388

D. 15.033

21) A public opinion poll surveyed a simple random sample of voters. Respondents were classified by gender and by voting preference-Republican, Democrat, or Independent. The results follow.

 

Voting Preferences                 Republican                  Democrat                    Independent                Row total

Male                200                  150                  50                    400

Female             250                  300                  50                    600

Column total               450                  450                  100                  1000

If you conduct a chi-square test of independence, what is the expected frequency count of male Independents?

 

A. 50

B. 60

C. 40

D. 30

22) What parametric test is equivalent to the nonparametric Spearman’s rank test?

A. T-test of correlation coefficient

B. T-test of two sample means

C. T-test of one sample mean.

D. T-test of two sample proportions

 

23) What is the variable used to predict another variable called?

A. Independent variable

B. Dependent variable

C. Moderating variable

D. Intervening variable

 

24) Michelle used a sample of 50 U.S. cities to estimate the relationship between crime, or annual property crimes per 100,000 persons, and income, or median income per capita. Her estimated regression equation was crime = 428 – .01 income. Assuming her model is statistically significant, if income decreases by $1,000, we would predict that crime will

A. decrease by 1

B. increase by 10

C. decrease by 10

D. increase by 100

 

25) 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. for each unit increase in ‘y’, ‘x’ increases by 25

D. the residual of ‘x’ factor

 

26) A test is conducted in eight cities to see if giving away free transit system maps will increase bus ridership. In a regression analysis, the dependent variable is the increase in bus ridership in thousands of persons from the start of the test until its conclusion. The independent variables are X1 = the number in thousands of free maps distributed and X2 = a binary equal to 1, if the city has free downtown parking and 0 otherwise. The estimated regression equation is Y = 1.32+.0345X1-1.45X2. If the Y value for city 3 is 7.3, X1 = 140, and X2 = 0 the residual for city 3 in thousands is:

A. 6.34

B. 1.15

C. .57

D. 2.01

 

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

A. $50,000 per year

B. $5,00 per month

C. $500,000 per year

D. $6,000 per year

 

28) 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. cyclical variation

C. seasonal variation

D. irregular variation          

 

29) A research company has been hired by a realty company to do an analysis of heating cost of homes in the region. The realty company wanted to be able to predict the heating cost of a typical single-family home. The realty company was constantly being asked questions regarding heating costs by potential home buyers. It was believed that these variables would impact heating costs (Y’): mean daily outdoor temperature (X1), the number of inches of insulation (X2), and the age in years of the furnace (X3). The multiple regression analysis produced the following regression equation: Y’ = 427.2 – 4.58X1 – 14.83X2 + 6.10X3. Which statement is correct based on this analysis?

A. The age of the furnace has an indirect relationship with heating costs.

B. There is an inverse relationship between outdoor temperature and heating costs.

C. There is no real clear relationship between these variables.

D. There exists a direct relationship between inches of insulation and heating costs.

 

30) If we fit a linear trend to data that are growing exponentially,

A. the fitted trend will be too high at the end

B. the forecasts, if extrapolated, will be too low

C. the forecasts, if extrapolated, will be too high

D. the fitted trend will be too low in the middle