A 99% confidence interval (in inches) for the mean height of a population is 65.67 < μ < 67.13. This result is based on a sample of size 144. If the confidence interval 65.87 < μ < 66.93 is obtained from the same sample data, what is the degree of confidence?

Confidence = 0.94 = 94%

Step-by-step explanation:

Solution:-

- A 99% confidence interval (in inches) for the mean height of a population is:

                                    65.44 < μ < 66.96

- If the confidence interval is obtained from the same sample data:

                                    65.65 < μ < 66.75

- The sample size, n = 144

- You will first need to find the sample mean (x_bar) and sample standard deviation (s) based on the confidence interval given. The width of the confidence interval is 2E  

                        2E = 66.96-65.44 = 1.52

                          E = 0.76

- The test statistic error (E) is defined as:

Where,     Z-critical for 99% confidence = 2.5758

- Since,  

                        x_bar - E = 65.44

                         x_bar = 65.44 - 0.76 = 66.2

- Use the value you found in part a to determine the degree of confidence for the interval 65.65 < μ < 66.75 is based on:

                         66.2 - E = 65.65

                         E = 0.55

- The test statistic error (E) is defined as:

- Determine the Z-critical value from equation above:

- The level of confidence for the corresponding Z-critical value would be:

                      Confidence =  P ( - z-critical < Z < z-critical )

                      Confidence =  P ( - 1.864 < Z < 1.864 )  

                      Confidence = 0.94 = 94%

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