We want to find out what the household size for U.S. states is with lower populations, basically less than 5 million people. We took a random sample of 11 states with lower populations which averaged a household size of 2.49 and a standard deviation of 0.1. The data showed no outliers or any problems. Using this information estimate the MEAN household size for U.S. states with lower populations with a 90% confidence.

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

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

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

4. 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

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

6. 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.

7. 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.