Question

A university with a high water bill is interested in estimating the mean amount of time that students spend in the shower each day. In a sample of 11 students, the average time was 5.33 minutes and the standard deviation was 1.33 minutes. Using this sample information, construct a 99% confidence interval for the mean amount of time that students spend in the shower each day. Assume normality.a) What is the lower limit of the 99% interval? Give your answer to three decimal places.

b) What is the upper limit of the 99% interval? Give your answer to three decimal places.

Answer 1

a) lower limit = 4.295 minutes

b) upper limit = 6.365 minutes

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 5.33 minutes

Standard deviation r = 1.33 minutes

Number of samples n = 11

Confidence interval = 99%

z(at 99% confidence) = 2.58

Substituting the values we have;

5.33+/-2.58(1.33/√11)

5.33+/-2.58(0.401010088288)

5.33+/-1.0346060277

5.33+/-1.035

= ( 4.295, 6.365) minutes

Therefore at 99% confidence interval (lower, upper limit) = ( 4.295, 6.365) minutes

a) lower limit = 4.295 minutes

b) upper limit = 6.365 minutes