1. An article on peanut butter in Consumer reports reported the following scores for various brands
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1 SMAM 314 Review Exam 1 1. An article on peanut butter in Consumer reports reported the following scores for various brands Creamy Crunchy Make a back to back stem and leaf display. Make the five number summaries and the boxplots. Use your calculator to find the means and the standard deviations. Comment on the shape of both data sets and the similarities and differences. Does one kind of peanut butter have a higher mean score than the other? Are the scores of one kind of peanut butter more dispersed. Are the data sets symmetric skewed or bell shaped? 2. A computer center studied the relationship between the time y to complete a job versus the estimated time x quoted to the customer. The following data in hours were obtained for five different jobs. Data Display Row x y Consider the scatterplot below * y * * * * x A. Basing your answer only on the scatterplot (1) Does a straight line model appear to be appropriate? Explain.
2 (2) Does the data appear to positively or negatively correlated? Explain. B. Using your calculator find the indicated quantities to fill in the blanks. (1) The regression line has slope and y intercept (2) The equation of the regression line is (3) The correlation coefficient is (4) The regression line accounts for % of the variation. C. Suppose that the center tells a customer that it will take 1.5 hours to complete a job. Use the regression equation to predict how long the job really will take. D. Does the straight line regression model appear to be a good one? Explain your answer in light of the quantities you have calculated. 3. No tortilla chip lover likes soggy chips. It is important to find characteristics of the production process that produce chips with an appealing texture. Data on frying time and moisture content of tortilla chips is given below Row fry time moisture Consider the scatterplot below * moisture * * 5.0+ * * * * * fry time A. Basing your answer only on the scatterplot (1) Does a straight line model appear to be appropriate? Explain. (2 points) (2) Does the data appear to positively or negatively correlated? Explain (2 points) B. Consider the MInitab output below Regression Analysis The regression equation is
3 moisture = fry time Predictor Coef Stdev tratio p Constant fry time s = Rsq = 65.7% Rsq(adj) = 60.0% Analysis of Variance SOURCE DF SS MS F p Regression Error Total Unusual Observations Obs. fry time moisture Fit Stdev.Fit Residual St.Resid R R denotes an obs. with a large st. resid. B. Fill in the blanks below by obtaining the information from the MInitab output (1) The regression line has slope and y intercept (2) The equation of the regression line is (3) The correlation coefficient is (4) The regression line accounts for % of the variation. C. Find the residual when the fry time is 20 minutes. (10 points) D. An alternative is to fit the model lny = a + bx instead of y = a + bx. The scatterplot of lny vs. x and the MInitab output are given below.
4 Character Plot 3.0+ * logmoist * 2.0+ * * * 1.0+ * * * fry time Regression Analysis The regression equation is logmoist = fry time Predictor Coef Stdev tratio p Constant fry time s = Rsq = 90.4% Rsq(adj) = 88.8% Analysis of Variance SOURCE DF SS MS F p Regression Error Total Write a paragraph explaining which of the two models is more useful and why. Base your answer only on the scatterplots and the Minitab outputs. 4. A video store sells two different brands of VCR, each of which comes with either two
5 heads or four heads. The table below gives the percentages of recent purchasers buying each type of VCR. Number of heads Brand 2 4 M 25% 16% Q 32% 27% A. What is the probability that a randomly selected purchaser (1) bought brand M with 2 heads? (2) bought brand M? B. Assuming a purchaser bought brand Q what is the conditional probability that he bought a VCR with 4 heads? 5. Consider the type of clothes dryer (gas or electric ) purchased by five different customers at an appliance store. The probability that all five purchase gas is The (probability that all five purchase electric is What is the probability that at least one dryer of each type is purchased? 6. The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability he must stop at the first signal is 0.4, the analogous probability for the second signal is 0.5 and the probability he must stop at at least one of the two signals is 0.6. A. What is the probability that he must stop (1) at both signals? (2) At the first signal but not the second signal? (3) At exactly one signal? (4) At none of the signals? B. What is the conditional probability that (1) a car stops at the second signal assuming he stopped at the first signal? (2) a car stops at the second signal assuming he did not stop at the first signal? (3)a car stopped at the first signal assuming that he stopped at the second signal? 7. An assembly plant receives microcircuits from three different suppliers A, B and C. Fifty percent are bought from A, 25 percent from each of B and C. The manufacturing plant defective for suppliers A, B and C are 5, 10 and 12 percent, respectively. A. Determine the probability that an assembled unit will contain a defective circuit. B. Determine the probability that an assembled unit came from supplier B if it is known that the circuit was good. 8. Consider the system of components connected as shown in the picture below. Components 1 and 2 are connected in parallel so the subsystem works if and only if either 1 or 2 works; since 3 and 4 are connected in series the subsystem works if and only if both 3 and 4 work. The two subsystems are connected in series. If components work independently of each other and the probability that each component works is 0.9 what is the probability that the system works?
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