Question

A sample of 16 is drawn for a normal population with an unknown population SD. The sample mean and the sample SD are calculated as 50 and 25, respectively. For a 95% confidence interval z0.025 and t0.025,15= 2.131. A 95% confidence interval for the population mean is equal to

Answer 1

The 95% confidence interval for the population mean is between 40.64 and 59.36.

Step-by-step explanation:

To calculate a 95% confidence interval for the population mean, we can use the formula:

(sample mean - (z * (sample standard deviation / √(sample size))), sample mean + (z * (sample standard deviation / √(sample size))))

Given that the sample mean is 50, the sample standard deviation is 25, and the sample size is 16, we can plug in the values to get the confidence interval:

(50 - (2.131 * (25 / √(16))), 50 + (2.131 * (25 / √(16))))

This simplifies to (40.64, 59.36), so the 95% confidence interval for the population mean is between 40.64 and 59.36.