ECON 2331 • ECONOMICS AND BUSINESS STATISTICS 2

PRACTICE EXAMINATION

PART A—Multiple-Choice Questions (30 marks total)

Please circle the letter of the correct answer directly on this exam paper. (1 mark each)

1.         The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is:

a.      2.447.

b.      1.943.

c.      2.365.

d.     1.985.

2.         The sum of the values of α and β:

a.      is always 1.

b.     is always .5.

c.      gives the probability of taking the correct decision.

d.     is not needed in hypothesis testing.

3.         What type of error occurs if you fail to reject H0  when, in fact, it is not true?

a.      Type II

b.     Type I

c.      either Type I or Type II, depending on the level of significance

d.     either Type I or Type II, depending on whether the test is one-tailed or two- tailed

4.         For a given sample size in hypothesis testing:

a.      The smaller the Type I error, the smaller the Type II error will be.

b.     The smaller the Type I error, the larger the Type II error will be.

c.      Type II error will not be effected by Type I error.

d.     The sum of Type I and Type II errors must equal to 1.

5.         If the null hypothesis is rejected in hypothesis testing:

a.      No conclusions can be drawn from the test.

b.     The alternative hypothesis is true.

c.      The data must have been accumulated incorrectly.

d.     The sample size has been too small.

6.         When the following hypotheses are being tested at a level of significance of α

H0: μ 500

Ha: μ < 500

the null hypothesis will be rejected, if the p-value is:

a.     ≤ α .

b.     > α .

c.      = α/2.

d.      1 - α/2.

7.         A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are:

a.      H0: μ ≠ 5.8     Ha: μ = 5.8.

b.     H0: μ = 5.8     Ha: μ ≠ 5.8.

c.      H0: μ > 5.8     Ha: μ ≤ 5.8.

d.     H0: μ ≥ 5.8     Ha: μ < 5.8.

8.         The sampling distribution for a goodness of fit test is the:

a.      Poisson distribution.

b.      t distribution.

c.      normal distribution.

d.     chi-square distribution.

9.         The number of degrees of freedom associated with the chi-square distribution in a test of independence is:

a.      number of sample items minus 1.

b.     number of populations minus 1.

c.      number of rows minus 1 times number of columns minus 1.

d.     number of populations minus number of estimated parameters minus 1.

10.       When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The expected frequency for each group is:

a.      .333.

b.      .50.

c.      1/3.

d.     50.

11.       The test statistic for goodness of fit has a chi-square distribution with k - 1

degrees of freedom provided that the expected frequencies for all categories are:

a.      5 or more.

b.      10 or more.

c.      k or more.

d.     2k.

12.       The ANOVA procedure is a statistical approach for determining whether or not the means of:

a.      two samples are equal.

b.     two or more samples are equal.

c.      two populations are equal.

d.     three or more populations are equal.

13.       In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is:

a.      133.2.

b.      13.32.

c.      14.8.

d.     30.0.

14.       When an analysis of variance is performed on samples drawn from k

populations, the mean square due to treatments (MSTR) is:

a.      SSTR/nT.

b.     SSTR/(nT - 1).

c.      SSTR/k.

d.     SSTR/(k - 1).

15.       In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is:

a.      200.

b.     40.

c.      80.

d.      120.

16.       In an analysis of variance, one estimate of σ2  is based upon the differences between the treatment means and the:

a.      Means of each sample.

b.     Overall sample mean.

c.      Sum of observations.

d.     Population means.

17.       Part of an ANOVA table is shown below.

Source of                              Sum of                Degrees of          Mean

Variation                              Squares              Freedom             Square           F

Between Treatments          180                      3

Within Treatments (Error)

TOTAL                                 480                       18

The mean square due to treatments (MSTR) is:

a.      20.

b.     60.

c.      18.

d.      15.

18.       If we are testing for the equality of three population means, we should use the:

a.      test statistic t.

b.     test statistic z.

c.      test statistic F.

d.     test statistic χ2.

19.       A test used to determine whether or not first-order autocorrelation is present is:

a.      serial-autocorrelation test.

b.      t test.

c.      chi-square test.

d.     Durbin-Watson Test.

20.       In multiple regression analysis, the general linear model:

a.      Cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.

b.     Can be used to accommodate curvilinear relationships between the independent variables and dependent variable.

c.      Must contain more than two independent variables.

d.     Cannot use the standard multiple regression procedures for estimation and prediction.

21.       Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model?

a.      a t test

b.      a z test

c.      an F test

d.     a chi-square test

22.       In regression analysis, the error term ε is a random variable with a mean or expected value of:

a.      0

b.      1

c.      μ

d.      x

23.       The coefficient of determination:

a.      Cannot be negative.

b.     Is the square root of the coefficient of correlation.

c.      Is the same as the coefficient of correlation.

d.     Can be negative or positive.

24.       If the coefficient of determination is a positive value, then the coefficient of correlation:

a.      Must also be positive.

b.     Must be zero.

c.      Can be either positive or negative.

d.     Can be larger than 1.

25.       In regression analysis, the unbiased estimate of the variance is:

a.      Coefficient of correlation.

b.     Coefficient of determination.

c.      Mean square error.

d.     Slope of the regression equation.

26.       Which of the following is not present in a time series?

a.      seasonality

b.     cross-sectional pattern

c.      trend

d.     cyclical pattern

27.       The component that reflects unexplained variability in the time series is called

a.      A trend component.

b.     Seasonal component.

c.      Cyclical component.

d.     Irregular component.

28.       The following linear trend expression was estimated using a time series with 17 time periods.

Tt = 129.2 + 3.8t

The trend projection for time period 18 is:

a.      68.4.

b.      193.8.

c.      197.6.

d.     6.84.

29.       The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effects is:

a.      Moving averages approach.

b.     Decomposition model.

c.      Simple linear regression.

d.     Qualitative forecasting method.

30.       Using a naive forecasting method, the forecast for next week’s sales volume equals:

a.      The most recent week’s forecast.

b.     The most recent week’s sales volume.

c.      Tthe average of the last four weeks’ sales volumes.

d.     Next week’s production volume.

PART B—Define/Describe/Distinguish (12 marks total)

In your own words, define/describe/distinguish between the following. Write your answers in one of the exam answer booklets. (3 marks each)

1.         Multiple Regression Analyses

2.         Time Series Analyses

3.         Tests for Goodness of Fit

Part C—Short-Answer Questions (38 marks total)

In one of the exam answer booklets, write your answers to all of the following questions (marks as indicated)

1.         Assume that the mean wage of employees is $25.00 and the standard deviation is $3.00. A sample of 36 employees finds a sample mean of $26.00. Conduct a test to determine if the mean wage is different from the population. (5 marks)

a.      State the null and alternative hypotheses

b.     Compute the standard error of the mea

c.      Compute the value of the appropriate test statistic

d.     Make a decision based on a critical z-value of 1.96

2.         The following two tables summarize the amount of time in minutes that it took an employee to drive to and from the office each day for one week. (6 marks)

a.      Name two possible ways to test if the amount of time it takes the employee to commute to and from work is different in the morning and late afternoon.

b.     How do the assumptions of these two methods differ?

c.      Which of these methods would be the most appropriate for this data?

3.         Telus wants to charge new consumers a premium to connect them if the service  person spends more than 15 minutes to connect the new customers. A sample of 36 connections indicate that the mean time is 17 minutes. Based on this sample should Telus charge a premium? The population standard deviation is 4 minutes. (6 marks total)

a.      State the null and alternative hypotheses and compute the value of the test statistic. (4 marks)

b.     What conclusion would you reach? Explain why? (2 marks)

Stock prices for 10 large corporations for last year and current year.

4.         Use the data above to conduct an appropriate test to see if the mean value of stock prices has changed between last year and the current year.  Level of significance α = 0.05. (6 marks)

5.         Complete the table, and test if there is sufficient evidence, at α = 0.05, that the population means corresponding to the treatments are not all equal. (6 marks)

6.         Vancouver’s Mayor claims that 20 percent of young people, aged 20-30, purchase condos rather than rent. A random sample of 200 of young people in this age group found that 56 had purchased condos. Use this sample result to test the hypothesis that more than 20 percent of young people buy rather than rent. Use a significance level of 0.01. (6 marks)

7.         Suppose a claim is made that wage rates for plumbers are higher than wage rates for electricians. You take random samples from both populations and compute the sample means. You apply the z-test for the difference of population means when the standard deviations of the two populations are known. You proceed to compute an interval estimate and get an interval of -$2.00 to +$3.50. Can you conclude that that wage rates for plumbers are higher than wage rates for carpenters? (3 marks)

Part D—Short-Answer Question (10 marks total)

Write your answer in one of the answer booklets.

Economists recognize that Investment is a positive function of GDP. Use the following sample data on GDP and Investment to answer the questions below.

Year  GDP (X)  Investment (Y)

1991     164,692           27,892

1992     178,660            28,840

1993     191,844           31,136

1994     210,196           37,544

1955     231,720           43,512

1996     259,272          50,604

1997     278,792           51,808

1998     304,524           52,788

1999     335,300          59,248

2000     360,716           62,500

2001     393,716           70,108

2002     439,652          78,644

2003     515,824           97,572

2004     616,152           121,180

2005     694,484          141,508

2006     799,976           160,556

2007     883,892           172,532

2008     979,508          189,284

2009      1,118,308        222,968

2010     1,257,560         255,044

2011     1,441,884          310,164

2012     1,519,436         284,300

2013     1,645,544        287,788

2014     1,798,328         300,820

2015     1,942,856         333,500

a.      Determine the regression equation using Investment as the dependent

variable. To use a calculator, use the equation given in the footnote on page 605 of your text.

b.     Can you determine if the coefficient on the GDP variable is statistically significant? Use the 0.05 significance level and an estimated standard deviation for the slope coefficient of 0.00540.

c.      Estimate what the level of investment would be if GDP were $800,000. Also construct a 95 percent confidence interval for this estimate. Assume that the estimated standard deviation of your estimated value for investment is $300.

Part E—Short-Answer Question (10 marks total) Write your answer in one of the answer booklets.

Use the following data to determine the seasonal index