Essay type Questions Chapter 9 (11 points each for Ch 9 essay type) 1. A sample of 25 items yields X = 50.0 grams and s = 2.5 grams. Assuming a normal distribution, construct a 99 percent confidence interval for the population mean weight. 2. Of a random sample of 600 trucks at a bridge, 120 had bad signal lights. Construct a 90 percent confidence interval for the percentage of trucks that had bad signal lights. 3. Suppose that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 3 percentage points of the actual proportion. Chapter 10 (11 points each for Ch. 10 essay type) 4. Test H0: 8 versus HA: > 8, at = 0.05 and 0.01, given n = 25, X = 8.07 and s = 0.16. Assume the sample is selected from a normally distributed population. 5. Test H0: = 0.2 versus H1: 0.2 with p = 0.28 and n = 100 at alpha = 0.05. 6. Test at =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system? Chapter 13 (16 points each for chapter 13 essay type) 7. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here): Brand Dell Hisense Hitachi JVC LG Maxent Panasonic Phillips Proview Samsung Price 2800 2800 2700 3500 3300 2000 4000 3000 2500 3000 Score 60 55 45 50 55 38 67 56 32 40 Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3800. 8. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model. X = 40 X2 = 200 Y = 70 Y2 = 545 XY = 300 Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation and check the relation between coefficient of correlation and coefficient of determination. Finally, perform the test of significance of the slope coefficient. Time Series forecasting (16 points) 9. Apply Holt-Winters Double exponential smoothing (without seasonality) to forecast the values of sales X for periods 13 and 14, using = 0.2 and = 0.3. Assume 12 months of sales data, as shown in the table below: Month t Sales Xt 1 152 2 176 3 160 4 192 5 220 6 272 7 256 8 280 9 300 10 280 11 312 12 328