Applied Engineering Statistics Assignment: Regression Analysis

This document presents a solution to an Applied Engineering Statistics assignment. The assignment addresses hypothesis testing, specifically comparing the hardness support of two tips using a t-test, and includes the calculation of a 95% confidence interval. The solution also covers regression analysis...Read More

Running head: APPLIED ENGINEERING STATISTICS
Applied Engineering Statistics
Name of the student:
Name of the University:
Author note:

1APPLIED ENGINEERING STATISTICS
Table of Contents
Answer to the question 1............................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................5
Part (c)....................................................................................................................................7
Answer to the question 2............................................................................................................7
Part (a)....................................................................................................................................7
Part (b)....................................................................................................................................8
Bibliography...............................................................................................................................9

2APPLIED ENGINEERING STATISTICS
Answer to the question 1
Part (a)
Figure 1 probability Plot of Tip 1

3APPLIED ENGINEERING STATISTICS
Figure 2 probability Plot of Tip 2

4APPLIED ENGINEERING STATISTICS
Figure 3 summary report of Tip 1

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Figure 4 summary report of Tip 2
From figure 1, 2 3 and 4 it is clear that the hardness tip support is normal and satisfy
the normality assumption. From probability plot it has been seen that the data pints are close
to the diagonal line. Hence it is normal. Moreover the figure 3 and 4 the histogram and
summary shows that the data is normal. Both the histogram are bell shaped.
Part (b)
Null hypothesis: There is no differences between the hardness support of Tip 1 and 2.
Alternative hypothesis: There is a differences between the hardness support of Tip 1 and 2.

6APPLIED ENGINEERING STATISTICS
Figure 5 t-test output
Test statistic = 0.40
Degrees of freedom = 13
P-value= 0.7
Alpha= 0.05
It is clear that the P-value > alpha> Hence the null hypothesis is not significant. There
for it may be summarized that there is no differences between the hardness support of Tip 1
and 2.

7APPLIED ENGINEERING STATISTICS
Part (c)
The 95% confidence interval is (-3.26, 4.76). The mean difference is 0.75. It defines
there is a differences between the mean of the hardness support of Tip 1 and 2.
Answer to the question 2
Figure 6 Regression output
Part (a)
Sale price= 13.32+3.3.24*taxes

8APPLIED ENGINEERING STATISTICS
Part (b)
It has been seen that the P-value is smaller than the alpha (at 5%). Hence it defines
that there is an association between the sales and taxes. Moreover the coefficient of
determination is 76.7%. It is a good regression model.

9APPLIED ENGINEERING STATISTICS
Bibliography
Kleinbaum, D.G., Kupper, L.L., Nizam, A. and Rosenberg, E.S., 2013. Applied regression
analysis and other multivariable methods. Nelson Education.
Lopez-Paz, D. and Oquab, M., 2016. Revisiting classifier two-sample tests. arXiv preprint
arXiv:1610.06545.