Question

In planning both market opportunity and production levels, being able to estimate the size of a market can be important. Suppose a diaper manufacturer wants to know how many diapers a one-month-old baby uses during a 24-hour period. To determine this usage, the manufacturer’s analyst randomly selects 17 parents of one-month-olds and asks them to keep track of diaper usage for 24 hours. The results are shown. Construct a 99% confidence interval to estimate the average daily diaper usage of a one-month-old baby. Assume diaper usage is normally distributed.

11	8	11	9	13	14	13
13	9	13	11	8	11	15
13	7	11

(Round the intermediate values to 3 decimal places. Round your answers to 2 decimal places.)

(blank) ≤ μ ≤ (blank)

Answer 1

The sample size is n = 17 . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	11	121
	8	64
	11	121
	9	81
	13	169
	14	196
	13	169
	13	169
	9	81
	13	169
	11	121
	8	64
	11	121
	15	225
	13	169
	7	49
	11	121
Sum =	190	2210

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The number of degrees of freedom are df = 24 - 1 = 23 , and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df = 23 degrees of freedom is t_c = 2.807

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

Ci = (11.176 - 1.332, 11.176 + 1.332)

CI= (9.84, 12.51)