A random sample of 90 observations produced a mean x?=

Chapter 6, Problem 4E

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QUESTION:

Problem 4E

A random sample of 90 observations produced a mean x̄= 25.9 and a standard deviation s= 2.7.

a. Find an approximate 95% confidence interval for the population mean μ.

b. Find an approximate 90% confidence interval for μ.

c. Find an approximate 99% confidence interval for μ.

Questions & Answers

QUESTION:

Problem 4E

A random sample of 90 observations produced a mean x̄= 25.9 and a standard deviation s= 2.7.

a. Find an approximate 95% confidence interval for the population mean μ.

b. Find an approximate 90% confidence interval for μ.

c. Find an approximate 99% confidence interval for μ.

ANSWER:

Answer:

Step 1 of 3:

         Given,

a). To find an approximate 95% confidence interval for the population mean

     For confidence coefficient 0.95, and

         (using the standard normal table, the z value for 95% CI is 1.96)

        That is,

      The confidence interval is

               

            

               

               (25.34, 26.46)

    Therefore, the confidence interval is (25.34, 26.46).


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