Question

2. A study of the thickness of a coating in microns yielded the 25 observations. A histogram, stem-and-leaf diagram and boxplot for these data is below: Coating Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N Stem and Leaf 7.664 0.7330757 0.1466151 7.9665988 7.3614012 25 85 9 9.5 10 Count Stem Leaf 9. 1 Quantiles maximum 9.9 9.9 لبا نے 100.0% 99.5% 97.5% 90.0% 75.0% 50.0% 25.0% 10.0% 2.5% 0.5% 0.0% 3 quartile median quartile 9 9 9 9 8 8 8455 83 8 001 7 889 7 67 7 455 7 23 7 0001 6 89 6 64 9.9 8.5 8.05 7.6 7.05 6.86 6.4 6.4 3 2 3 2 2 minimum 6.4 1 Summary Statistics 64 represents 6.4 a) Suppose that upon investigation it is found that one of the data points is flagged as an unusual data point due to an irregularity in the process. What should be done with this data point? b) Explain what the 95% CI on the average thickness of the coating represents. c) Would you be surprised to hear a claim that this average is 7.7 microns? Explain based on the CI.

Answer 1

a)As we can see from the stem and leaf plot the sample data is mainly concentrated between 6.4 to 8.5,there is only one sample point which is 9.1,so probably this is an outlier relying on the sample quality andignoring the particular irregularity.

So it should be removed from the data,in order to avoid further problems.

b)95% confidence interval on the average thickness of coating represents the interval in real numbers say (l1,u1), within which we can find the mean 95% of times the sample points are collected or available. That is if the underlying assumptions are true then within the points l1 and u1 we can expect simply that out of 100 times,95 times the mean should be present.

c)I won't be surprised because upper CI is 7.966 and lower CI is 7.3614 and 7.7 is witin them, so it's natural to have the mean being that quantity.