Discuss the importance of constructing confidence intervals

Question

Part -1:

1. Discuss the importance of constructing confidence intervals for the population mean.
o What are confidence intervals?
o What is a point estimate?
o What is the best point estimate for the population mean? Explain.
o Why do we need confidence intervals?

2. Based on your selected topic, evaluate the following:
o Find the best point estimate of the population mean.
o Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and ÏÆ' is unknown.
     Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
o Write a statement that correctly interprets the confidence interval in context of your selected topic.

3. Based on your selected topic, evaluate the following:
o Find the best point estimate of the population mean.
o Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and ÏÆ' is unknown.
      Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
o Write a statement that correctly interprets the confidence interval in context of your selected topic.

4. Compare and contrast your findings for the 95% and 99% confidence interval.
o Did you notice any changes in your interval estimate? Explain.
o What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.

Part -2:

1.) Find the critical value χ_L² corresponding to a sample size of 19 and a confidence level of 99%.

2.) Find the critical value χ_R² corresponding to a sample size of 19 and a confidence level of 99%.

3.) The values listed below are the waiting times (in minutes) of customers at the Bank of Providence, where customers enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation and write a statement that correctly interprets the results.

4.2

5.4

5.8

6.2

6.7

7.7

8.5

9.3

10

4.) You want to estimate σ for the population of waiting times at a fast-food restaurant's drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of σ. Find the minimum sample size needed. Is this sample size practical?