The 2006 General Social Survey contains information on the number of years of education that respondents have completed. The data are presented below. (Note: throughout the exercise, answers may vary due to rounding.)
- What are the steps involved in calculating confidence intervals as they were discussed in Chapter 8?
- Let's calculate a 99 percent confidence interval for the total sample of respondents described in the table. In order to do this, we must first calculate the standard error of the mean. Do we have enough information in order to do this? Why or why not?
- Suppose we were to estimate the value of the standard error of the mean. What would be the value of this quantity?
- Using your answer from Question #4, calculate a 99 percent confidence interval for the mean number of years of education for the total sample.
- In examining your work on Question #4, suppose you decide to calculate confidence intervals for each of the three racial groups as originally presented in the table at the outset of these questions. Calculate a 95 percent confidence interval for whites.
- Calculate a 95 percent confidence interval for blacks.
- Calculate a 95 percent confidence interval for those of other races.
- In Chapter 8 we introduced the idea of there being a tradeoff between the confidence and precision of our confidence intervals. Demonstrate this tradeoff by recalculating your answer to Question #7, only this time at 68 percent confidence. Discuss your results.
- In Chapter 8 we also introduced the idea that increasing the sample size results in greater precision of confidence intervals. Demonstrate this relationship by recalculating your answer to Question # 6, only this time with a sample size of 4,725. Discuss your results.
- For this final question, your task is to calculate the most precise confidence interval possible for the total sample. You must choose one of the following confidence levels: 68%, 95%, or 99%. You must also select one of the following sample sizes: 100, 1,000, or 10,000. Be sure to discuss your rationale for choosing a particular level of confidence and a particular sample size.
- Suppose the total sample size was increased. Based on the ideas introduced in Chapter 8, how would the confidence intervals be affected?
- Calculate a 99 percent confidence interval for the mean number of years of education for the total sample. Interpret the results.