Question 24 For obtaining a 99% Confidence Interval for the difference of the means of two normal populations, two random samples, one from each population, both equal to 19, were drawn. For the first sample, sample mean = 22, and sample standard deviation = 14.58. For the second sample, sample mean = 35, and sample standard deviation = 10.29. Assuming both populations have the same variance, the pooled estimate of the population standard deviation is: 0 28.5 0 8.29 12.62 0 12.44 Question 25 Table of correlation Coefficients Gross Attendance Playing weeks New Productions Gross 1.000 Attendance 0.905 1.000 Playing weeks 0.873 0.977 1.000 New Productions 0.775 0.411 0.375 1.000 Before building a multiple regression model with data on four variables, we obtained the table of correlation coefficients above. If we ran a simple regression model with "Gross" as the response variable and "New Productions" as the predictor variable, the proportion of variability explained by the regression model will be (fraction rounded to two places of decimal): 0.6 Question 26 A soap manufacturer tested a bar of soap to see how long it would last. A test subject showered with the soap each day for 15 days and recorded the weight (in grams) of the soap after the shower. A regression model with Weight as the Response variable, and Days as the predictor variable, the model was able to explain 84.4% of the variability in soap weight. The regression line would clearly have a negative slope. The correlation coefficient between these two variables is: 0.919 0 -0.712 0.712 -0.919 Question 27 Partial Excel output from another random sample of 10 observations Multiple R R Square Regression Statistics Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept df SS MS F Significance F 230.8 350.4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 3.508 9.795 0.681 Number of salespeople working (x) 0.319 The R Square value is equal to (rounded to two places of decimal): 0.34