3.3)  Confidence interval for the mean of a dataset

The dataset below contains MgO concentrations for speciality glass batches manufactured over a period of several 
years. There are stringent quality requirements and the MgO content has to be between 7.3 and 7.5 mass% or the 
company faces expensive penalties. 

A. Determine if the data fit a normal distribution by using histograms and the normal probability plot. 

B. Calculate the mean and median, and a Bootstrapped 95% confidence window on these. Does the company have 
a problem? 

C. How many samples plot outside the 7.3 - 7.5 % window, and what is the percentage of the total samples. How 
does this compare to the answer in B, and, if different, why is this? 

D. Use the t-distribution estimate of the 95% confidence level on the mean as discussed in last week’s lecture. How 
does this compare to the answers in B and C, and, if different, why is this?

E. What is the best estimate of the true confidence level on the MgO content in your opinion, and why? 

MgO (mass%)
6.9
5.8
7.3
6.6
6.5
7.3
6.8
8.2
6.3
8.5
7.9
5.8
7.2
8.8
7.8
7.7
6.3
6.4
6.5
7.6
7.2
7.4
6.8
9.5
3.1
8.9
8.7
8.1
8.4
6.8
7.1
6.5
6.8
9.3
5.7
7.0
7.7
7.2
6.0
7.5
9.4
5.9
7.6
7.4
6.3
7.9
7.0
7.7
6.8
7.2
7.9
6.8
8.1
6.3
7.3
7.3
5.8
7.3
6.4
7.0
7.4
8.6
6.8
7.1
6.5
8.1
6.7
7.0
7.3
5.8
6.3
4.6
10.1
6.5
5.7
5.8
8.0
6.3
8.0
8.3
5.6
6.6
7.6
8.1
8.7
8.6
5.8
10.1
7.8
8.5
7.3
6.1
5.4
6.7
6.5
6.5
7.2
6.4
8.0
6.6
6.3
6.7
7.7
6.4
6.3
6.0
9.5
7.1
7.1
6.4
5.9
6.5
7.8
5.6
8.5
6.5
7.9
5.8
6.7
7.6
5.5
6.6
7.0
7.0
7.7
6.3
7.5
6.7
5.4
5.6
7.2
6.1
7.1
7.5
8.1
6.2
6.4
5.9
6.0
6.6
6.5
7.3
9.9
8.4
7.0
7.0
6.5
8.0
7.6
6.0
8.2
6.5
8.1
7.1
8.6
7.4
7.8
7.7
7.7
7.6
8.6
7.2
5.9
8.9
8.3
7.1
8.6
6.2
6.9
6.1
6.2
7.5
7.0
7.6
8.8
9.8
6.7
6.0
7.2
9.2
7.6
6.0
7.9
8.5
8.4
7.5
6.0
10.1
10.3
9.5
5.0
10.9
6.4
5.6
8.6
7.0
6.9
5.2
5.6
5.7
6.2
8.3
6.3
7.4
8.0
8.6
7.3
8.2
7.7
8.0
8.7
7.3
9.1
7.5
9.7
8.8
8.9
5.7
6.0
7.4
8.5
7.1
6.7
6.4
6.6
7.2
6.3
7.8
6.7
10.2
6.2
7.2
7.8
9.3
7.9
8.6
7.0
5.2
6.2
7.3
6.4
6.8
6.3
6.7
7.1
8.2
6.3
7.1
7.5
7.5
8.9
8.9
8.7
8.8
9.8
6.6
8.7
7.1
6.9
7.6
7.1
5.9
7.8
7.9
7.3
7.5
6.8
7.0
8.8
6.6
7.5
6.0
6.6
5.6
7.5
6.6
8.2
7.1
6.1
7.3
7.5
8.1
8.2
7.7
6.6
5.6
6.2
7.6
7.1
7.9
7.2
7.1
8.3
2.6
2.4
7.7
7.8
7.8
7.7
7.2
7.4
8.1
8.4
8.3
8.5
6.5
6.9
8.4
8.2
7.4
10.2
9.5
7.6
7.3
7.2
6.8
5.4
7.5
8.1
6.8
8.0
8.8
7.7
7.9
7.7
7.0
7.4
7.7
7.7
6.1
6.3
7.2
7.4
8.2
8.7
9.3
8.2
7.9
7.2
7.3
6.6
6.4
6.3
5.8
5.9
7.8
7.0
6.8
6.5
5.8
7.0
7.1
8.7
6.3
7.7
6.7
7.4
9.3
7.5
6.0
8.8
8.3
6.5
7.4
7.9
7.8
6.1
6.5
8.3
8.8
7.3
5.7
7.9
7.3
7.0
9.0
7.6
7.8
6.8
8.9
6.4
8.6
7.9
6.8
7.7
7.2
7.1
6.8
6.8
6.7
5.9
7.3
7.3
7.3
5.9
7.7
6.0
6.6
7.8
6.5
8.5
7.2
8.0
6.4
8.5
7.2
5.8
4.1
11.6
7.6
7.4
8.3
7.0
7.2
6.4
7.5
7.0
5.7
7.8
6.1
8.3
5.9
8.2
6.5
7.6
8.2
6.7
7.7
7.4
6.8
7.5
5.4
7.1
9.8
6.2
5.8
8.0
8.9
6.2
9.0
7.7
8.2
7.1
5.2
8.7
8.8
7.5
8.0
6.1
8.2
8.7
7.8
7.9
8.3
5.5
7.7
7.6
7.4
7.3
7.5
9.2
7.4
8.9
9.0
8.3
8.0
7.1
7.4
7.9
8.5
8.7
7.7
7.3
7.3
7.2
8.9
6.3
7.8
6.4
7.6
5.6
7.8
6.8
4.5
9.0
7.4
6.9
7.7
7.4
7.3
7.1
6.9
7.6
7.5
8.1
6.8
9.1
7.5
5.9
8.4
6.5
6.3
8.7
8.4
6.8
5.9
5.6
7.7
8.0
6.9
8.9
6.0
7.9
8.4
6.7
6.0
7.4
7.6
6.4
7.2
7.7
7.2
7.0
9.0
6.1
7.9
6.8
7.7
7.3
7.8
7.2
7.2
7.8
7.6
8.6
10.2
8.4
9.3
8.3
8.4
4.8
8.9
7.7
7.9
6.6
7.5
6.5
8.2
7.4
7.6
7.0
8.0
7.4
8.8
6.8
8.4
6.9
6.8
6.5
6.3
9.6
6.2
2.8
2.5
10.5
7.0
9.4
9.1
7.0
6.7
8.9
9.0
9.3
8.6
8.7
7.6
7.7
8.8
6.8
6.8
9.3
8.2
7.9
8.2
9.5
8.7
9.8
9.8
10.5
8.0
7.8
8.3
9.2
8.6
6.9
6.6
6.7
7.6
8.5
7.2
8.2
7.7
8.3
8.6
7.5
8.9
8.5
7.1
7.5
8.5
8.6
9.0
7.9
6.2
8.9
6.3
6.4
6.5
9.1
5.6
7.6
9.4
7.7
9.3
9.3
8.0
8.7
7.8
8.4
7.9
8.3
9.1
8.1
9.0
7.1
7.3
6.5
7.9
8.3
8.5
9.4
10.5
9.4
11.0
7.9
5.8
8.7
7.7
7.9
6.6
9.3
7.2
7.3
7.2
7.4
7.8
6.5
7.5
8.5
6.4
6.9
7.3
7.2
5.9
8.4
7.7
8.3
8.4
5.9
7.0
8.3
9.5
8.0
6.5
6.8
10.1
7.5
10.4
7.0
7.0
7.1
8.5
7.9
6.0
7.3
6.1
7.5
6.7
10.4
6.6
8.1
10.6
8.3
6.7
8.4
7.5
8.8
10.7
7.1
8.2
7.1
8.4
7.6
8.7
7.8
8.5
9.1
6.2
7.7
7.1
7.3
7.6
5.6
7.0
6.4
8.3
8.0
8.9
6.8
7.3
7.4
6.3
8.1
8.0
9.3
7.9
7.6
7.4
6.8
7.0
7.4
8.6
8.3
7.9
8.2
7.8
8.1
7.3
8.3
6.4
8.2
7.0
7.3
8.2
7.9
6.7
5.7
3.0
8.0
9.1
6.8
5.5
7.1
7.2
6.5
5.8
7.6
8.4
6.8
6.7
6.5
5.3
6.5
8.4
7.3
7.5
6.6
5.0
6.2
6.0
6.7
9.0
7.4
7.8
9.7
7.3
7.2
7.4
6.7
7.1
6.4
6.2
7.5
9.7
8.3
8.9
6.7
6.2
6.7
8.0
8.4
7.8
8.0
6.1
6.6
8.9
6.4
5.9
7.1
8.7
6.2
7.5
8.9
7.8
7.7
7.0
6.7
7.2
10.5
6.8
8.9
6.7
7.1
8.4
7.4
8.3
7.5
8.4
7.8
6.5
6.8
6.5
6.0
8.0
7.6
8.3
6.4
7.5
6.8
7.1
5.6
7.5
7.4
8.9
6.7
5.8
6.5
6.5
8.5
7.9
7.9
6.4
6.4
7.0
8.0
6.1
6.8
9.3
7.8
8.8
6.4
9.3
6.1
6.5
5.7
8.3
6.6
7.8
6.9
7.5
8.0
7.2
7.2
7.2
5.7
7.5
8.5
7.7
8.0
8.0
7.6
7.0
6.8
10.0
9.0
8.2
7.8
10.4
7.2
7.2
9.1
8.6
8.8
7.0
10.3
6.8
6.4
5.7
8.4
6.3
7.9
7.6
10.3
6.2
6.5
7.3
9.1
6.9
8.4
9.0
8.1
11.7
7.3
6.7
6.2
6.9
7.2
7.8
9.0
9.0
7.4
7.1
7.2
6.9
7.5
8.4
7.9
7.9
7.6
7.3
6.8
6.6
6.8
5.6
9.1
8.2
7.1
7.0
8.7
7.6
8.0
7.9
8.5
7.4
6.4
8.2
7.6
9.0
4.6
6.4
7.6
7.3
7.5
8.2
6.7
8.2
8.3
6.6
10.7
9.1
6.6
7.3
7.7
7.1
6.1
6.6
4.8
6.6
7.7
7.3
6.9
7.9
8.1
7.5
7.6
5.8
8.0
7.2
7.8
7.5
7.1
7.6
7.8
8.0
7.7
6.6
7.3
6.9
7.8
6.9
7.3
8.1
6.2
7.0
8.0
6.8
8.5
7.6
7.0
6.3
7.8
5.8
6.6
6.8
7.9
7.1
6.3
7.6
9.2
8.0
7.0
8.5
8.1
6.5
8.4
7.2
7.0
7.0
9.4
8.0
8.1
7.7
6.4
6.9
9.7
6.3
6.8
7.3
7.1
7.5
8.3
9.7
8.0
6.8
8.1
8.4
8.5
7.6
6.5
8.1
6.9
8.0
9.1
8.4
7.2
7.4
9.5
6.3
6.4
7.2
7.7
6.4
7.4
8.1
9.2
10.2
9.3
9.7
6.8
8.5
6.7
6.8
10.1
6.8