Question

Suppose we are interested in calculating a 95% confidence interval for the mean of a normally distributed population. We've drawn a sample of 8 observations from this population, and found a sample mean of 304.5 and a sample standard deviation of 38.0.What is the appropriate lower endpoint of the 95% interval for mu?

Answer 1

To calculate the lower endpoint of a 95% confidence interval for the mean of a normally distributed population, you need to subtract the margin of error from the sample mean. In this case, the lower endpoint is approximately 272.494.

Step-by-step explanation:

To calculate the lower endpoint of a 95% confidence interval for the mean of a normally distributed population, we can use the formula:

Lower endpoint = sample mean - margin of error

Given that we have a sample mean of 304.5 and a sample standard deviation of 38.0, we need to calculate the margin of error. The margin of error can be calculated using the formula:

Margin of error = critical value * standard deviation / sqrt(sample size)

Since the sample size is 8, the critical value for a 95% confidence interval is 2.306. Plugging in these values, we get:

Margin of error = 2.306 * 38.0 / sqrt(8)

Simplifying this gives a margin of error of approximately 32.006. Therefore, the lower endpoint of the 95% confidence interval for mu is:

Lower endpoint = 304.5 - 32.006 = 272.494