ECO 578 FINAL EXAM SUMMER II 2016 Page 1 of 12 Name: _________________________ ID: _________________________ Online Final Exam Final Exam There are 4...

Part A: Fill in the blank (1-26)

1) The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) __________________ concerning a (an) _______________ by examining the data contained in a (an) _______________ from that ____________________.

2) A hypothesis may be defined simply as __________________________________________.

3) There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.

4) The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis.

5) The _____________ hypothesis is the hypothesis that is tested.

6) If the null hypothesis is not rejected, we conclude that the alternative _________________.

7) If the null hypothesis is not rejected, we conclude that the null hypothesis _____________.

8) A Type I error occurs when the investigator _____________________________.

9) A Type II error occurs when the investigator _____________________________ .

10) The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________.

11) Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.

12) The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as____________ as or more _______ than that actually obtained is less than or equal to , the null hypothesis is____ _________. Otherwise, the null hypothesis is ______________________ .

ECO 578 FINAL EXAM SUMMER II 2016 Page 2 of 12

13) The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ____________ for the ________________test.

14) When one is testing H0: μ= μ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of σ2 , the test statistic is __________________________________.

15) When one is testing H0: μ= μ0 on the basis of data from a sample of size n from a normally distributed population with a unknown variance, the test statistic is _____________________________________.

16) The null hypothesis contains a statement of __________________________________.

17) The statement μ ≥ 0 is an inappropriate statement for the ____________ hypothesis.

18) The rejection region consists of those values of the ______________ that will cause rejection of the null hypothesis.

19) The null hypothesis and the alternative hypothesis are ____________ of each other.

20) Given , H0: μ= μ0, then Ha : ___________________________________ .

21) Given H0: μ ≤ μ0, then Ha : ___________________________________ .

22) Given H0: μ ≥ μ0, then Ha : ___________________________________ .

23) A statement of what you wish to conclude goes in the ______________.

24) A market analyst believes that more than 30% of the adults in a certain area regularly read a certain magazine. The analyst wishes to conduct a hypothesis test to see whether this belief will be supported. The appropriate statistical hypotheses are: __________________.

25) Given: H0: μ ≥ 50; Ha: μ < 50; α = 0.05. A simple random sample of size 64 is drawn from a non-normally distributed population. ????̅= 45, s2 = 256. The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution.

26) Given: H0: μ= 100; Ha: μ ≠ 100; α = 0.03; computed z = 2.25, p = 0.0244. The null hypothesis should reject because __________________________________________.

Part B: Use questions number 27-50 from page 9-54 to 9-57 to write your answer below (27-50).

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Part C: Please fill in the blank and answer the following questions (51-53).51. Use problem 14 on page 14-13 to fill in the table and answer the following questions.SourceSSdfMSFTreatments________________Error____________Total________ANSWERa) What is the hypothesis being tested in this problem?b) In the above ANOVA table, is the factor significant at the 5% level?c) Number of observations?52. Use problem 16 on page 14-13 to fill in the table and answer the following questions.SourceSSdfMSFTreatments________________Error____________Total________ANSWERa) What is the hypothesis being tested in this problem?b) In the above ANOVA table, is the factor significant at the 5% level?c) Number of observations?53. If ????2=0.95, n=11, and Σ(????−????̅)2=100, what is ????????2? (Single Regression model)ECO 578 FINAL EXAM SUMMER II 2016 Page 4 of 12Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed (54-67).54. Given the following probabilities, find Z0 and please draw the shading the areaShow your workPlease draw graphsa.P(????≤????0)=0.2090b.P(−1.67≤????≤????0)=0.8844c.P(????>????0)=0.0455=d.P(????0≤????≤3.02)=0.0009e.P(????>????0)=0.7224f.P(−????0≤????≤????0)=0.1664ECO 578 FINAL EXAM SUMMER II 2016 Page 5 of 1255. Work on problem number 28 (a-d) on page 7-26a)b)c)d)56. Work on problem number 13 (a-c) on page 7-48a)b)????)ECO 578 FINAL EXAM SUMMER II 2016 Page 6 of 1257. A sample of size n = 10 is randomly selected from a normal population with mean μ = 52 and variance ????2= 22.5. The sample value ????̅ is calculated.a) ????(????̅>55)=?b) ????(50≤????̅≤60)=?c) ????(????̅≤55)=?58. Use problem number 12 on page 8-11 to answer the following questions (a-d)a) Meanb) Variancec) Standard deviationd) Find a 90% confidence interval for the mean μ. Interpret this intervalECO 578 FINAL EXAM SUMMER II 2016 Page 7 of 1259. Please fill in the computer printout and answer the following questions (a-b).Given that α=0.05SUMMARY OUTPUTRegression StatisticsMultiple R0.9037R Square______Adjusted R Square______Standard Error______Observations______ANOVAdfSSMSFSignificance FRegression14.9____________0.03535Residual31.1______Total____________CoefficientsStandard Errort StatP-valueLower95%Upper 95%Lower 95.0%Upper 95.0%Intercept-0.1______-0.157460.88488________________________X10.7______3.65563______________________________a) Predicting Y given that X=5; confidence interval ????=0.05b) Estimating mean given that X=5; confidence interval ????=0.05ECO 578 FINAL EXAM SUMMER II 2016 Page 8 of 1260. The following regression equation was obtained using the five independent variables.Given that ????=0.05CoefficientsStd. Errort-StatP-valueIntercept729.8665169.257514.31216590.0010099Price-10.8873.4952397-3.11480780.0089406Advertising0.04650.01762282.63862970.0216284ANOVAdfSSMSFSignificance FRegression212442.86221.437.561279940.00000683Residual121987.6165.63333Total1414430.4Se =12.86986 R-sq = 0.862263 R-sq(adj) = 0.8393068a)Write the multiple regression equationb)Interpret the multiple regression equationc)What is the standard error of estimate? Can you use this statistic to assess the model’s fit? If so, how?d)Which independent variable appears to be the best predictor of sales? Explain.e)What is the number of observations used in this study?f)What is the coefficient of determination, and what does it tell you about the regression model?g)Assuming that the coefficient on Advertising has Ha: B1 > 0, what statistical decision should be made at 5% level.h)Conduct a global test of hypothesis to determine if any of the regression coefficients are not zeroECO 578 FINAL EXAM SUMMER II 2016 Page 9 of 1261. Work on problem 3 on page 10-27 and answer the following questions (a-d)a) Write the estimated regression equation.b) What is the number of sample in this study?c) Use a t test to determine whether monthlymaintenance expense is related to usage at the .05level of significance.d) Use the estimated regression equation to predictmonthly maintenance expense for any terminal thatis used 25 hours per week.62. A metropolitan bus system sampler’s rider counts on one of its express commuter routes for aweek. Use the following data to establish whether the rider ship is evenly balanced by day ofthe week. Let  = 0.05.Day Monday Tuesday Wednesday Thursday FridayRider Count 10 34 21 57 44a) What is you hypothesis testingb) What is your ????2?c) Is the χ2 value significant at the 5 % level of significance?d) Write the conclusion for this question.ECO 578 FINAL EXAM SUMMER II 2016 Page 10 of 1263. Work on problem 13 on page 15-10a) What is you hypothesis testingb) What is your ????2?c) Is the χ2 value significant at the 10 % level of significance?d) Write the conclusion for this question.64. Consider the following hypothesis testHo: μ ≥ 10Ha: μ < 10A sample of 50 provides a sample mean of 9.46 and sample variance of 4.a)At 5% should the null be rejected?b)Compute the value of the test statistic 2c)What is the p-value?d)What is your conclusion?ECO 578 FINAL EXAM SUMMER II 2016 Page 11 of 1265. Work on problem 2 on page 11-9a)b)c)66. Work on problem 2 on page 10-23a)b)c)d)e)ECO 578 FINAL EXAM SUMMER II 2016 Page 12 of 1267. Use problem 15 on page 10-32 to answer the following questionsa)Find ????1b)Find ????0c)Write the equationd)Find ????2e)Find SSTf)Find ????????g) Construct the 95% confidence interval for the mean of y when x = 7h) Construct the 95% confidence interval for the individual value of y when x = 9