Question

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25, The upper limit of a 95% confidence interval for the population means would equal. (Specify your answer to the 3rd decimal.)

Answer 1

To find the upper limit of a 95% confidence interval for the population mean, calculate the standard error by taking the square root of the sample variance divided by the square root of the sample size. Then, find the critical value for a 95% confidence interval, which is approximately 1.96. Finally, use the formula to calculate the upper limit by adding the product of the critical value and the standard error to the sample mean.

Step-by-step explanation:

To find the upper limit of a 95% confidence interval for the population mean, we can use the formula:

Upper Limit = Sample Mean + (Critical Value) * (Standard Error)

First, we need to calculate the standard error, which is the square root of the sample variance divided by the square root of the sample size. In this case, the sample variance is 25 and the sample size is 15, so the standard error is sqrt(25/15) = 1.6667.

Next, we need to find the critical value for a 95% confidence interval. The critical value can be found using a Z-table or a calculator. For a 95% confidence interval, the critical value is approximately 1.96.

Finally, we can plug in the values:

Upper Limit = 75 + (1.96) * (1.6667) = 78.3

Therefore, the upper limit of a 95% confidence interval for the population mean is 78.3 (rounded to the 3rd decimal place).