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Chi-Square test by hand

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See the attached file.

1. What would be the mean of the test statistic if the null hypothesis were true? The value of the statistic is so far above this mean that you can see at once that it must be highly significant. What is the approximate P value?

2. Look at the terms of the chi-square statistic and compare observed and expected counts in the cells that contribute the most to chi-square. Based on this, write a short comparison of the differences in self-evaluation of health for current smokers and nonsmokers.

BHMC 343
Applied Statistics for Healthcare Managers
Two-Way Table for Exercise 3.4

Current Smoker
Health Yes No
Excellent 25 484
Very Good 115 1557
Good 145 1309
Fair 90 545
Poor 29 11.

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Solution Summary

This solution is comprised of a detailed explanation for the relationship between two categorical variables such. Chi-Square analysis with the help of Excel is performed. Null and Alternative Hypothesis are defined properly followed by the results and interpretation part. The calculations were done by hand and valid conclusion as per the hypothesis is provided.

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See attached files.

1. What would be the mean of the test statistic if the null hypothesis were true? The value of the statistic is so far above this mean that you can see at once that it must be highly significant. What is the approximate P value?
Solution:
The mean of the test statistics is 0 because the mean difference is -3.000 and test statistics value is -3.000. Since the value of the test statistics is large so we can say that it is highly significant. The approximate P-value is 0.017.

2. Look at the terms of the chi-square statistic and compare observed and expected counts in the cells that contribute the most to chi-square. Based on this, write a short comparison of the differences in self-evaluation of health ...

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