A) Two Sample Tests 1) Philips claims that their hundred watt light bulbs last longer than Sylvania's. They collect 40 of their own light bulbs and 40 of the light bulbs produced by Sylvania and measure the lengths of life (in hours) for both samples. This is in file \"Bulb1s\". Is Philips correct? Conduct an appropriate test to t and explain if they are or not and why (Pick you own alpha value) ___________________________________________________________________________________ 2) The manufacturer of Boston and Vermont asphalt shingles knows that product weight is a major factor in the customer's perception of quality. Moreover, the weight represents the amount of raw materials being used and is therefore very important to the company from a cost standpoint. The last stage of the assembly line packages the shingles before they are placed on wooden pallets. Once a pallet is full (a pallet for most brands holds 16 squares of shingles), it is weighed and the measurement is recorded. The file \"Pallet\" contains the weight (in pounds) from a sample of 368 pallets of Boston shingles and 330 pallets of Vermont shingles. Is there a difference in the weights of the Boston and Vermont shingles? (Pick your own alpha value) ___________________________________________________________________________________ 3) AMS communicates with customers who subscribe to cable television services through a special secured email system that sends messages about service changes, new features, and billing information to in-home digital set-top boxes for later display. To enhance customer service, the operations department established the business objective of reducing the amount of time to fully update each subscriber's set of messages. The department selected two candidate messaging systems and conducted an experiment in which 15 randomly chosen cable subscribers were sampled. The update process for each subscriber email was measured for each of the two messaging systems. The data is in file \"AMS10\". Is there a difference in these two messaging systems? Conduct the appropriate test and analyze the results (pick your own alpha) ___________________________________________________________________________________ 4) A hotel manager looks to enhance the initial impression that hotel guests have when they check in. Contribution to initial impressions is the time it takes to deliver a guest's luggage to the room after check-in. A random sample of 20 deliveries on a particular day were selected in Wing A of the hotel, and a random sample of 20 deliveries were selected in Wing B. The results are in file \"Luggage\". Is Wing A worse than Wing B? Conduct the appropriate test and analyze the results (pick your own alpha value B) Concepts: Pick the best choice for each of these questions (These 10 questions are worth 2 points each): 1) A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each two tests: one given after two hours' sleep and one after eight hours' sleep. The test the researcher should use would be: A) T-test for the differences in two means assuming equal variances B) T-Test for the differences in two means assuming unequal variances C) Paired t-test D) F test for the differences in variances E) Any of the above Page 1 of 5 --------------------------------------------------------------------------------------------------------------------------2) The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. A study was conducted to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. The 95% confidence interval estimate for the difference in the two means is -0.9543 1 - 2 1.3593. At this level of confidence, this indicates that with respect to amount of time required to reach a customer service representative: A) There is no difference between the two hotels. B) There is a difference between the two hotels with hotel one being slower than hotel two C) There is a difference between the two hotels with hotel two being slower than hotel one D) Not enough information to come to a conclusion ------------------------------------------------------------------------------------------------------------------------------3) In the regression equation, the Y-intercept represents the A) predicted value of Y when X = 0. B) change in estimated Y per unit change in X. C) predicted value of Y. D) variation around the sample regression line. ---------------------------------------------------------------------------------------------------------------------------4) Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables. A) TRUE B) FALSE --------------------------------------------------------------------------------------------------------------------------5) The value of r (the correlation coefficient) is always positive. A) TRUE B) FALSE ---------------------------------------------------------------------------------------------------------------------------6) If the correlation coefficient (r) = 1.00, then A) all the data points must fall exactly on a straight line with a slope that equals 1.00. B) all the data points must fall exactly on a straight line with a negative slope. C) all the data points must fall exactly on a straight line with a positive slope. D) all the data points must fall exactly on a horizontal straight line with a zero slope. ----------------------------------------------------------------------------------------------------------------------------- 7) In a simple linear regression problem, r (correlation coefficient) and b1 (slope) A) may have opposite signs. B) must have the same sign. C) must have opposite signs. D) are equal. -----------------------------------------------------------------------------------------------------------------------------8) An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. Page 2 of 5 SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA Regression Residual Total df 2 7 9 Intercept GDP Price Coeff -0.0861 0.7654 -0.0006 SS 33.4163 0.6277 34.0440 MS 16.7082 0.0897 StdError 0.5674 0.0574 0.0028 F 186.325 t Stat -0.152 13.340 -0.219 Signif F 0.0001 p-value 0.8837 0.0001 0.8330 When the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression? A) 98.2 B) 11.1 C) 2.8 D) 1.1 --------------------------------------------------------------------------------------------------------------------------Use the following information for questions 9 and 10 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: Page 3 of 5 Page 4 of 5 9) Which of the following is the correct interpretation for the slope coefficient? A) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands. B) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands. C) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands. D) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands. 10) Which of the following assumptions appears to have been violated? A) Normality of error B) Equality of Variances C) Independence of errors D) None of the above --------------------------------------------------------------------------------------------------------------------------- Page 5 of 5