Question

Use the following sample to estimate a population mean . 20.9 23.4 5.9 39.4 19.8 22.6 27 36.4 7.8 assuming the population is normally distributed, find the 99.9% confidence interval about the population mean. enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places. 99.9% c.i. = incorrect

A) (lower limit, upper limit)

B) (18.22, 35.58)

C) (21.67, 33.11)

D) (20.05, 34.73)

E) (22.91, 31.87)

Answer 1

To estimate a population mean, we calculate the sample mean and standard error. Using a t-distribution table, we find the critical value for the 99.9% confidence level. Multiplying the critical value by the estimated standard error gives us the margin of error.

Step-by-step explanation:

To calculate a 99.9% confidence interval about the population mean, we first need to calculate the sample mean and the standard error. The sample mean is the average of the sample values, which in this case is 22.96. The standard error is calculated by dividing the standard deviation by the square root of the sample size. Since we don't have the standard deviation of the population, we can estimate it using the sample standard deviation, which is 11.77, divided by the square root of the sample size, which is 9. The estimated standard error is 3.92.

Next, we need to calculate the margin of error. The margin of error is the product of the critical value and the estimated standard error. The critical value can be found using a t-distribution table with a 99.9% confidence level and degrees of freedom equal to the sample size minus 1. In this case, the critical value is 4.61. Multiplying the critical value by the estimated standard error gives us a margin of error of 18.01.

Finally, we can calculate the confidence interval. Subtracting the margin of error from the sample mean gives us the lower limit, and adding the margin of error gives us the upper limit. So the 99.9% confidence interval about the population mean is (4.95, 41.97).