SMAM 314 Exam 49 Name. 1.Mark the following statements true or false (10 points-2 each)

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1 SMAM 314 Exam 49 Name 1.Mark the following statements true or false (10 points-2 each) _F A. When fitting a least square equation it is necessary that the observations come from a normal distribution. Fitting least square equation is a Calculus problem not a statistics problem. F B. A fuel economy study is conducted for two types of automobiles to see if one kind gets more miles per gallon than another kind. Five observations are available concerning the performance of each kind of car. A paired t test on the differences is appropriate. The two kinds of cars are independent random samples. T_C. A 95% confidence interval is obtained on the ratio of the variabilities of the measurements of readings taken by two measuring instruments. The hypothesis that the variabilities are equal is rejected when the confidence interval does not contain 1. This corresponds to the F statistic being in the rejection region. F D. A correlation coefficient of.0961 means that there is a strong linear correlation between two variables. This correlation coefficient is near zero meaning linear correlation is very weak. T E. When testing for equality of proportions using the normal probability table the sample sizes must be large. The test is based on the central limit theorem. 2. Ten engineering schools in the US were sampled. The sample contained 250 electrical engineers, 80 being women, 175 chemical engineers 40 being women. A. Find a 99% two sided confidence interval on the difference in the proportion of women in these two kinds of engineering. (10 points) ) p 1 = =.32,) p 2 = =.229 ( ) ± (.32)(.68) ± (.229)(.771) 175 (.021,.203) B. Based only on the confidence interval would you reject the null hypothesis H 0 p 1 = p 2 in favor of H 1 p 1 p 2 at α =.01. Explain your answer. (5 points) The confidence interval contains zero so H 0 would not be rejected.

2 3. Are average daily hotel rates significantly higher in New Orleans than Minneapolis?The following data is obtained by taking hotel rate samples from the two cities Minneapolis New Orleans n M = 22 n NO = 20 x M = $112 x NO = $122 s M = $11 s NO = $12 A. Determine whether the hotel rates are higher in New Orleans by doing an appropriate test of hypothesis. Assume equal standard deviations.(20 points) H 0 µ m = µ no H 1 µ m < µ no Assumptions Independent random samples Normal populations Unknown but equal standard deviations Region of rejection Reject H 0 at α =.05 if T< Calculation of test statistic 21(121) + 19(144) s 2 p = = s p = T = = = 2.81 Reject or do not reject Reject H 0 at α =.05 Answer the original question. There is significant evidence that hotel rates are higher in New Orleans. B. Find a 95% confidence interval on the ratio of the variances of the cost of hotels in New Orleans to that in Minneapolis. Is the assumption of equal variances justified? Explain. (10 points) (2.49),144(2.44) 121 (.00478,2.904) The confidence interval contains 1 so the hypothesis of equal variances is justified.

3 4. A study is conducted to determine whether there is a difference in bus ridership between morning and afternoon rush hours. The transit authority s researcher randomly selects nine buses because of the variety of routes they represent. On a given day the number of riders on each bus is counted at 7:45 AM and at 4:45 PM with the following results. Bus Morning Afternoon A. Using the results in the computer printout below write the report of the test of hypothesis that determines whether there is a significant difference in ridership between the morning and afternoon. Use α =.05 (20 points) Paired T for Morning - Afternoon N Mean StDev SE Mean Morning Afternoon Difference T-Test of mean difference = 0 (vs not = 0): T-Value = P-Value = H 0 µ D = 0 H 1 µ D 0 Assumptions Paired differences Differences are normally distributed. Region of rejection p value less than.05 Reject H 0 if T >2.306 or T < Valueof test statistic T = -.30 Pvalue =.772 Reject or do not reject Cannot reject H 0 Answer the original question. There is not enough evidence to conclude there is a difference in bus ridership between morning and afternoon.

4 B. Find a 95% confidence interval on the difference between morning and afternoon bus ridership. Do the results appear to be consistent with the test of hypothesis performed above. Explain your answer. (10 points).44 ± 2.306(4.45) / 9.44 ± 3.42 ( 3.86,2.98) The confidence interval contains zero so the results are consistent. 5. People in the aerospace industry believe the cost of a space project is a function of the weight of the major object being sent into space. Consider the data below. Weight(tons) Cost($millions) $

5 A. Based only on the scatterplot does a straight line model appear to be appropriate?explain.(2 points) A straight line model might be appropriate because the points are not too scattered away from a straight line. B.Based on the scatterplot does the data appear to be positively or negatively correlated? Explain. (2 pots) The data is positively correlated. As weight increases so does cost. C. Using your hand held calculator to do the computations complete the following statements. (1)-(5) 1 point each (6) and (7) 3 points each (1) The slope of the least square regression line is (2) The y intercept of the least square regression line is 39 (3) The equation of the least square regression line is y = 66.36x+39 (4) The correlation coefficient is.9518 (5) The regression line accounts for _90.6 % of the variation.

6 (6) The regression equation would predict that a 2 ton object costs million dollars. (7) The residual (difference between the observed and the predicted value) when x=1.058 is C. Based on the above information is a linear model appropriate for this data. Explain your answer. (5 points) The scatterplot is close to the straight line. The regression accounts for 90% of the variation and the correlation coefficient is A linear model appears to be appropriate.

SMAM 314 Exam 3 Name. 1. Mark the following statements true or false. (6 points 2 each)

SMAM 314 Exam 3 Name. 1. Mark the following statements true or false. (6 points 2 each) SMAM 314 Exam 3 Name 1. Mark the following statements true or false. (6 points 2 each) F A. A t test on independent samples is appropriate when the results of an algebra test are being compared for the