Question

Based on a sample of 100 customers, a company constructed a confidence interval with a 90% confidence level of (25.1, 114.3) for the mean annual income of its customers, in thousands of dollars per year. Check all of the following that are true about the confidence interval:

	Calculation of the confidence interval assumed annual income is normally distributed.
	There is a 90% chance that the mean annual income of the customer population is between 25.1 and 114.3.
	The confidence interval would change if the company constructed it from a different sample of 100 customers.
	An 80% confidence interval calculated from the same sample would result in tighter confidence interval.

Answer 1

Solution;-

False - Calculation of the confidence interval assumed annual income is normally distributed.

The distribution for the mean annual income is not mentioned.

True - There is a 90% chance that the mean annual income of the customer population is between 25.1 and 114.3.

False - The confidence interval would change if the company constructed it from a different sample of 100 customers.

Approximately same confidence interval would be obtained.

True - An 80% confidence interval calculated from the same sample would result in tighter confidence interval.

The value for confidence coefficient for 80% confidence level would be smaller than confidence coefficient for 90% confidence level, hence 80% confidence interval calculated from the same sample would result in tighter confidence interval.