Week 7 Homework Problems

a. b. Using Excel’s in-built slope function, the slope of the regression equation is Thus; Slope = 1.6606 Similarly, using Excel’s in-built intercept function, the y-intercept is y-Intercept = = 69.739% The regression equation for the percentage of GDP spent on health expenditure, and the percentage of women receiving prenatal care is y = 1.6606x + 69.739% For a country that spends 5.0% of GDP on health expenditure y = 1.6606*5% + 69.739% = 8.303% + 69.739% = 78.04% Thus, percent of women receiving prenatal care is 78.04% For a country that spends 12.0% of GDP on health expenditure y = 1.6606*5% + 69.739% = 19.927% + 69.739% = 89.67% Thus, percent of women receiving prenatal care is 89.67% c. Using Excel’s in-built correl function, the correlation coefficient is

∑ x 2 = 1.034 Df= = (2 – 1)(4 – 1) = 3 Significance level = 0.05 Using chi-square tables, Probability, Pr ( x 2 ( 3 ) 0.05 > 1.034 ) ≈ 0.7930 Since the p-value is greater than the significance level (0.01), we fail to reject the null hypothesis. We can, therefore, conclude that there is sufficient statistical evidence to indicate that cardiovascular disease is in the same proportion as all deaths for the different age groups. 11.2.6 A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in the table. Table: Reason for Choosing a Car Safety Reliability Cost Performance Comfort Looks 84 62 46 34 47 27 Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level. P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = P ( 5 ) = 1 6 Expected Frequency = n ∗ p = 300 ∗ 1 6 = 50 ∑ x 2 = 42.2 Df- = (6 – 1) = 5 Significance level = 0.05 Using chi-square tables, Probability, Pr ( x 2 ( 5 ) 0.05 > 42.2 ) ≈ 5.366 E − 8 Since the p-value is less than the significance level (0.01), we reject the null hypothesis. We can, therefore, conclude that there is sufficient statistical evidence to indicate that the reasons for choosing a car are equally likely among safety, reliability, cost, performance, comfort, and looks.