Question

12. The 95% confidence interval for a population mean is between 6.3 and 7.7. What was the mean

of the sample and margin of error that led to this confidence interval?

Answer 1

The mean of the sample was of 7 and the margin of error was of 0.7.

Explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction between the bounds divided by 2.

In this question:

Lower bound: 6.3

Upper bound: 7.7

Mean of the sample is the point estimate, so: (6.3+7.7)/2 = 7

Margin of error: (7.7-6.3)/2 = 0.7

The mean of the sample was of 7 and the margin of error was of 0.7.