Question

1. 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.  

2. A company produces a women's bowling ball that is supposed to weigh exactly 14 pounds. Unfortunately, the company has a problem with the variability of the weight. In a sample of 11 of the bowling balls the sample standard deviation was found to be 0.71 pounds. Construct a 95% confidence interval for the variance of the bowling ball weight. Assume normality.

a) What is the lower limit of the 95% interval? Give your answer to three decimal places.  

b) What is the upper limit of the 95% interval? Give your answer to three decimal places.  

c) Which of the following assumptions should be checked before constructing the above confidence interval?

-the data need to be right skewed

-the data need to follow a normal distribution     

-the data need to have small variance

-the data need to follow a chi-square distribution

Answer 1

c.

The data need to follow a normal distribution