Question

A random sample of 100 stores from a large garden supply chain was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. A 95% confidence interval was calculated to be 5.62 < μ < 6.38 based on the sample statistics. The confidence interval may be interpreted as follows.

	A.	95% of the stores have sold between 5.62 and 6.38 lawnmowers on average.
	B.	There is a 95% probability that the sample mean number of lawnmowers sold is between 5.62 and 6.38.
	C.	If all possible samples of 100 are taken from the population, 95% of the confidence intervals developed will include the population mean.
	D.	If all possible samples of 100 are drawn from the population, 95% of the sample means will fall between 5.62 and 6.38.

Answer 1

Answer: D. If all possible samples of 100 are drawn from the population, 95% of the sample means will fall between 5.62 and 6.38.

The confidence level is the probability that the calculated confidence interval estimate will contain the true population parameter. The confidence level is the percent of confidence intervals that contain the true population parameter when repeated samples are taken. Eg. 95% confidence interval means, then with 95% confidence that the true value of the population mean is within the interval.