QUESTION 7 In a recent interview, the producers of "Big Brother" claimed that one-third of the 15 to 24 age group regularly watch reality TV shows. A UQ academic wishes to test this claim as part of a book she is writing on the social impact of reality TV. From a survey of 350 people in this age group, it was found that 132 regularly watched reality TV shows. Assume that the survey data were collected through a random sample and use 5% level of significance. 1. State the direction of the alternative hypothesis used to test the producers' claim. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Calculate the test statistic (two decimal places) 3. Use the tables in the textbook to determine the p-value for the test, giving your answer to four decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Disregarding your answer for 4, ifthe null hypothesis was rejected, would the producers' claim appear to be valid at the 5% level? Type yes or no. QUESTION 1 The government introduced new laws requiring long distance truck drivers to take minimum rest breaks. Prior to introducing the new laws, the true proportion of long distance truck drivers who often felt tired while driving was 70%. A statistics student wanted to test whether the proportion of long distance truck drivers who often feel tired while driving had been reduced (below 70%) 6 months after the introduction the new laws. The student calculated the Z-test statistic based on a sample and found it was -2.25. What is the p-value for this test? 0 a- 0.9878 0 ID0.0122 O C- 0.0244 0 d0.4989 1 points QUESTION 2 1 points Save Answer Which of the following is TRUE? O a. The p-value should always be larger than the selected level of significance. O b. If the p-value is smaller than the level of significance, then do not reject the alternate hypothesis. O C. If we reject the null hypothesis, it is possible that p-value is larger than the selected level of significance. O d. If the p-value is larger than the level of significance, then do not reject the null hypothesis.QUESTION 3 3 points Save Answer A regression analysis of male MBA graduates finds that taller persons tend to be offerred higher starting salaries upon graduation. In this situation, the independent variable is O height O being male O salary O none ofthe above QUESTION 4 2 points Save Answer The Maroochy Chamber of Commerce is interested in determining the relationship between the number of fine days each year and the number of interstate and overseas tourists visiting the Sunshine Coast each year, measured in thousands. Using annual data from 1993 to 2005 (inclusive), the following model was estimated: Y = 8.88 +1.04 X Error sum of squares: 544.9 Sum of squares of X: 973.4 Determine the lower limit for the 90% condence interval for the slope correct to two decimal places. QUESTION 5 2 points Save Answer df SS Regression Residual 67 51.61 Total 68 106.87 The ANOVA table above is from a simple linear regression analysis relating the percentage alcohol content in diferent brands of beer to the number of kilojoules per 100mL. Determine the coefficient of determination as a percentage, correct to two decimal places.Question completion status: QUESTION 6 SU M MARY OUTPUT Regression Statistics Multiple R 0.90 R Squared 0.80 Adjusted qu 0.79 Standard Error 82.06 Observations 19.00 ANOVA df Regression 1 Residual 17 Total 18 Coefficients Intercept 756.26 Age -10.27 This output was obtained from data on the age of houses (in years) and the associated amount paid in rates (:5). Predict the rates paid (in dollars correct to two decimal places) for a house that is 23.0 years old. 55 467247.53 1144662 581713] St Error 30.41 1.23 MS 4672475 67333 t Stat 24.87 -8.33 2 points Save. qucsuull LUIIIHICLIUl I JLGLUJ. QUESTION 7 5 points Save Answer A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 65 countries (n) over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors for be and b1 are reported in parentheses under the coefficients b0 and b1 Yhat = 5.272 - 0.0047 X (1.463) (0.0035) To test the significance ofthe relationship, a 5% level of significance was adopted. 1. State the direction of the alternative hypothesis used to test the statistical significance of the relationship. Type gt (greater than). ge (greater than or equal to), It (less than), le (less than or equal to) or he (not equal to) as appropriate in the box. 2. Calculate the test statistic. reporting your answer to two decimal places. 3. Use the tables in the textbook to determine the critical value for this test (in absolute terms) to three decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Disregarding your answer in part 4, ifthe null hypothesis was not rejected, would there appear to be a linear relationship between resource abundance and economic growth? Type yes or no, ' An environmental economist wished to determine the market demand function for tradable permits in carbon dioxide emissions from experimental data she had collected. Using 1 3 different values for the price per tonne in dollars (P), the following was estimated: Q = 6022.5 5.833 P Standard error of the estimate: 378.42 Sum of squares of price: 4268'] .0 where Q is the number of thousand tonnes of carbon dioxide demanded at the price P. 1. State the direction of the alternative hypothesis used to test that the demand function is downward sloping. Type gt (greater than), ge (greater than or equal to), It (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Use the tables in the textbook to determine the critical value used to conduct the test, assuming a 5% level of significance. lf doing a two tail test, state only the positive value to three decimal places. 3. Calculate the test statistic, reporting your answer to two decimal places. 4. Is the null hypothesis rejected for this test? Type yes or no. 5. Disregarding your answer in part 4, if the null hypothesis was rejected, would the demand curve for tradable permits be downward sloping? Type yes or no. QUESTION 9 A US consumer lobby wishes to develop a model to predict gasoline mileage, as measured by miles per gallon, based on the horsepower ofthe car's engine. The Excel data file AUTO.xls (contained in a folder under the CML Quizzes tab) contains data on this for fifty recent models. Use Excel Data Analysis to estimate a linear model for the relationship, the 94% confidence interval and the residual plot. State all numerical answers correct to four decimal places using the excel output results: 'I. the intercept , 2. the slope coefficient , and 3. the coefficient of determination, 4. Using this model, predict the gasoline mileage for the car with 85 horsepower. Use all decimal places in your calculation by selecting and using the values of be and b1 in the output generated by Excel. 5. Does the prediction involve extrapolating the relationship? Type yes or no. Use Excel to determine a 94% confidence interval for the slope coefficient, reporting the 6. lower bound 7. upper bound for the interval, correct to 4 decimal places. 7 points Save