Lab TA:_______________ID:_________________Name:___________________ Soc 3811 Basic Social Statistics Extra Credit A total of 20 points 1. The following table presents the total sample size and the percentage distribution of a grouped variable, “Hours of Shopping this Year.” Calculate the mean and the variance. Note that you need to find “frequency (fi)”, “midpoint (Yi)”, and “deviation (di)” for each row before you can get the mean and the variance. Hours Shopping Percentage (%) Frequency (fi) Midpoint (Yi) Deviation di2 di2(fi) 1-4 5 5-8 25 9-12 15 13-16 30 17-20 5 21-24 20 Total 100.0 550 Mean___________ Variance___________ 2. One of the Stat’s TA’s believes that cats are more popular than dogs. Test the hypothesis using the data within the data tables provided below. Cats Popularity Freq Percent Cum. % low 15 75 75 high 5 25 100 Total: 20 Dogs Popularity Freq Percent Cum. % low 22 68.75 68.75 high 10 45.45 100 Total: 32 1: State the research and null hypothesis in symbolic form. 2: Perform a T-test. 3: Find the critical value of T relative to the .05 alpha level. 4: Make a decision relative to the null hypothesis and interpret the result. 3. The following equation is a predicted regression line based on an analysis of a sample of 2,500 people. “Happiness” is the dependent continuous variable measured by a 100 point happiness scale. Income is a dummy variable, 0 for low-income, 1 for middle-income, and 2 for upper-income. Happiness = a + b * Income Here is the STATA output: Happiness Coefficient St. Error t P>t Income 22.45 4.76 7.65 .000 Constant 19.1 4.09 2.25 .029 Observations = 2500 F(1, 2498) = 13.32 Prob > F=.0001 R^2 = .217 Adj. R^2= .201 Answer the following questions. 1. Are the variables happiness and income related, and if so, by how much? How do you know this? 2. What is the strength of this relationship? Happiness = a + b * Income+ b * Health - b * Age The above equation is a predicted multivariable regression line based on an analysis of a sample of 2,500 people. “Happiness” is the dependent continuous variable measured by a 100 point happiness scale. Health is a continuous measure, scored 0 (poor health) to 10 (excellent health). Income is a dummy variable, 0 for low-income, 1 for middle- to upper-income. Age is a continuous measure and is measured in years. Here is the STATA. Happiness Coefficient St. Error t P>t Income 15.6 3.76 3.65 .001 Health 10.4 1.77 3.09 .001 Age -5.9 .87 2.76 .01 Constant 19.1 4.09 2.25 .029 Observations = 2500 F(1, 2498) = 9.44 Prob > F= .0001 R^2 = .381 Adj. R^2= .341 Answer the following. 3. Compare the coefficients from this model to the bivariate model above. How are they different, and why do you think they are different? Which is a better model? 4. Write the predicted equations for both the bivariate and multivariate regressions. ...