We suspect that Method 1 for detecting impurities in iron ingots yields higher results than Method 2 for finding such impurities. We want to give a 95% confidence interval for the difference in the average number of impurities detected by the two methods. In order to obtain the confidence interval, we measured the impurities of 3 ingots, employing both methods for each ingot. The results are presented in the table below. We let 1 denote the population average number of defects for Method 1 and 2 denotes the population average number of defects for Method 2. We wish to develop a confidence interval for ??=?1−?2μd=μ1−μ2 Give the margin of error for the 95% confidence interval for ??=?1−?2μd=μ1−μ2 Ingot 1 Ingot 2 Ingot 3 Method 1 16 32 12 Method 2 12 26 10
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.
We suspect that Method 1 for detecting impurities in iron ingots yields higher results than Method 2 for finding such impurities. We want to give a 95% confidence interval for the difference in the average number of impurities detected by the two methods. In order to obtain the confidence interval, we measured the impurities of 3 ingots, employing both methods for each ingot. The results are presented in the table below.
We let 1 denote the population average number of defects for Method 1 and 2 denotes the population average number of defects for Method 2. We wish to develop a confidence interval for ??=?1−?2μd=μ1−μ2
Give the margin of error for the 95% confidence interval for ??=?1−?2μd=μ1−μ2
| Ingot 1 | Ingot 2 | Ingot 3 | |
| Method 1 | 16 | 32 | 12 |
| Method 2 | 12 | 26 | 10 |
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