1 Final Exam Review Sheet 2 Directions: Answer the following questions using the formulas on page seven as a reference. The Institute for Racial Equality in Education is interested in knowing if there exists a racial disparity in education in the United States. Suppose that U.S. census data showed that, nationally, the population of adult (age 18 +) Americans had a mean education of 13.27 years in the year 2002. Imagine that sample data for white non-institutionalized English-speaking adults from the 2002 General Social Survey revealed that a random sample of 50 whites had a mean education of 13.16 years with a standard deviation of 3.352 years. Use this information to answer questions 1 - 6. 1. Test the hypothesis that the true population mean education for whites is different from the national population mean for all American adults. Use an alpha level of .05. Make certain to follow the five steps in hypothesis testing.2 2. Suppose that we had reason to believe that the mean education for whites was actually less than the national population mean for all American adults. Conduct this test use an alpha level of .05. Describe how this test is different or identical to the last test. Repeat any of the five steps in hypothesis testing that differ from the last test or otherwise state that there is no difference in the step.3 3. Suppose that we used a 0.10 level of significance to perform our last test. Would it have changed our results? Describe how this test is different or identical to the last test (performed for question 2). Repeat any of the five steps in hypothesis testing that differ from the last test or otherwise state that there is no difference in the step. 4. Suppose that we were told that the true population standard deviation for whites was equal to 2.992. Conduct the same test as you preformed for question 1, using the true population standard deviation to calculate the standard error of the sampling distribution. Describe how this test is different or identical to the last test (performed for question 1). Repeat any of the five steps in hypothesis testing that differ from the last test or otherwise state that there is no difference in the step.4 5. Using the population standard deviation (given in question 4), construct the 95 percent confidence interval for the sample mean education for whites. Interpret your results. 6. Using the population standard deviation (given in question 4), construct the 90 percent confidence interval for the sample mean education for whites. Interpret your results.5 Suppose that we discovered that 905 GSS respondents in 2002 watched television for an average of 3 hours per day, with a standard deviation of 2.4 hours. Answer the following questions, assuming that the distribution of the number of TV hours is normal. 7. What proportion of people watch television less than 5 hours per day? 8. What proportion of people watch between 1 and 6 hours of television hours per day?6 Useful Formulas Z = YSYY − MYY∑=µ NYYσσ= CI = Y ± Z(Yσ) Z = NYYYσµ− t = NSYYYµ− df = N –