Confidence Intervals:

What is the average household size for U.S. states with lower populations (less than 5 million people)? A random sample of 11 states with lower populations resulted in an average household size of 2.49 with a standard deviation of 0.1. A plot of the data showed no outliers or cause for concern. Estimate the mean household size for U.S. states with lower populations with 90% confidence. Answer the following questions in a complete sentence.

1. State the name of the appropriate estimation procedure.

2. Describe the parameter of interest in the context of the problem.

3. Name the conditions for the procedure.

4. Explain how the above conditions are met.

5. Write down the confidence level and the t* critical value.

6. Calculate the margin of error for the interval to three decimal places. Show your work.

7. Calculate the confidence interval to three decimal places and state it in interval form. Show your work and correct formula.

8. Interpret your confidence interval in context. Do this by including these three parts in your conclusion (3 pts): Level of confidence Parameter of interest in context The interval estimate

9. How would selecting a 95% level of confidence change the size of the calculated confidence interval? Explain or justify your answer by recalculating.

10. At a 95% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of 0.05? Use = 0.2. Show your work and correct formula.

11. Suppose that a second random sample of household size was conducted. Using this sample, the confidence interval was calculated to be (2.31, 2.88) people. Rounded to two decimal places, what is the margin of error for this confidence interval? Show your work.