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. 13 8 11 9 13 14 12 12 9 13 11 8 11 15 12 7 13

____ ≤ μ ≤ ___

Answer 1

Given that the diaper usage is normally distributed. However, population standard deviation is unknown. So, we need to use t-distribution to calculate confidence interval.

Number of samples, n= 17

Degrees of freedom, df= n-1 =16

Confidence interval is given by,

,

where,

is the sample mean, s is the sample standard deviation and n is the number of samples.

s= 2.31

From t-table, t-value for 99% confidence with 16 degrees of freedom is 2.921

Confidence interval is,