# Use the applet Confidence Intervals for a Mean (the impact of confidence level) to investigate...

Use the applet Confidence Intervals for a Mean (the impact of confidence level) to investigate the situation in Exercise 6.5 further. For this exercise, assume that  = 2.62 is the population mean and  = 4.1 is the population standard deviation.

a. Using n = 70 and the normal distribution with the mean and standard deviation above, run the applet one time. How many of the 95% confidence intervals contain the mean? How many would you expect to contain the mean? How many of the 99% confidence intervals contain the mean? How many would you expect to contain the mean?

b. Which confidence level has a greater frequency of intervals that contain the mean? Is this result what you would expect? Explain.

c. Without clearing, run the applet several more times. What happens to the proportion of 95% confidence intervals that contain the mean as you run the applet more and more? What happens to the proportion of 99% confidence intervals that contain the mean as you run the applet more and more? Interpret these results in terms of the meanings of the 95% confidence interval and the 99% confidence interval.

d. Change the distribution to right skewed, clear, and run the applet several more times. Do you get the same results as in part c? Would you change your answer to part e of Exercise 6.5 ? Explain.

Exercise 6.5

A random sample of 70 observations from a normally distributed population possesses a sample mean equal to 26.2 and a sample standard deviation equal to 4.1.

a. Find an approximate 95% confidence interval for .

b. What do you mean when you say that a confidence coefficient is .95?

c. Find an approximate 99% confidence interval for .

d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

e. Would your confidence intervals of parts a and c be valid if the distribution of the original population was not normal? Explain.

Jul 22 2021| 12:56 PM |
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}