sample Al St 1 8.1 8 2 4.9 8.1 3 8.4 8.2 4 6.9 7.4 5 6.1 7.6 6 7.2 7 7 6.2 6.9 8 6.6 8.2 9 6.7 8.3 10 5.3 7.9 11 8.6 8.7 12 7.7 9.7 13 6 7.5 14 9.1 5.8 In a manufacturing application, a aluminum alloy is replacing a previous steel alloy as the main structural component. In order to maintain the same performance, it is important to assess whether or not the new alloy has the same coefficient of thermal expansion (CoTE) as the previous material. (a) Perform a hypothesis test to determine if their is strong evidence for the claim that there is a difference in the CoTE for these two materials to α = 0.01 level.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
| sample | Al | St |
| 1 | 8.1 | 8 |
| 2 | 4.9 | 8.1 |
| 3 | 8.4 | 8.2 |
| 4 | 6.9 | 7.4 |
| 5 | 6.1 | 7.6 |
| 6 | 7.2 | 7 |
| 7 | 6.2 | 6.9 |
| 8 | 6.6 | 8.2 |
| 9 | 6.7 | 8.3 |
| 10 | 5.3 | 7.9 |
| 11 | 8.6 | 8.7 |
| 12 | 7.7 | 9.7 |
| 13 | 6 | 7.5 |
| 14 | 9.1 | 5.8 |
In a manufacturing application, a aluminum alloy is replacing a previous steel alloy as the main
structural component. In order to maintain the same performance, it is important to assess whether
or not the new alloy has the same coefficient of thermal expansion (CoTE) as the previous material.
(a) Perform a hypothesis test to determine if their is strong evidence for the claim that there is a
difference in the CoTE for these two materials to α = 0.01 level.
(b) Construct a 95% confidence interval for the difference in the two population mean CoTE, µ1 −µ2.
(c) Construct a plot that supports your results from part (a)
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