Question

Write an analysis (essay) for question

2) The table summarizes the results from an observational study that followed a random sample of 8,474 people for about four years. All participants were free from heart disease at the beginning of the study. The variable Anger categorizes participants as Low Anger, Moderate Anger, High Anger based on the Speilberger Trait Anger Scale test, which measures how prone a person is to sudden feelings of anger. CHD stands for coronary heart disease, which is a count of the people who had heart attacks or needed medical attention for heart disease during the study.

	Low Anger	Moderate Anger	High Anger	Total
CHD	53	110	27	190
No CHD	3,057	4,621	606	8,284
Total	3,110	4,731	633	8,474

Research Question:

Does this data suggest that there is an association between anger and heart disease?

Your analysis will include the following:

A Statements of the research question

A description of the source of the data

A description of the variables used in the analysis

A contingency table (two-way table)

Calculations of relevant percentages

Answer to the question based on your analysis of the data.

Answer 1

Statement of research question:

To check whether there is an association between the anger and heart disease.

Description of the source of data:

This data consists of 8474 responses of people. There are 2 categorical variables Anger and heart disease.

Description of the variables used in the analysis:

Here there are two categorical variables as anger and heart disease, anger variable has three categories like low, moderate and high and heart disease has two categories like CHD and No CHD. So the check the association between both Chi-square test will use.

A contingency table(two wat table) is already given in the problem.

Calculations of relevant percentage:

Analysis of the data:

To check the association between the two variables with the larger population, let us use a Chi-square test of association.

The null and alternative hypothesis for the test are:

The formula of test statistics is:

Where O - observed frequencies and E - Expected frequencies

The formula of expected frequencies is:

The expected frequencies are:

CHD, Low

CHD, Moderate

CHD, High

No CHD, Low

No CHD, Moderate

No CHD, High

By plug in all the values in the formula of test statistics,

Chi-square critical value:

Level of significance is not given, take it as 0.05

Degrees of freedom = (number of row categories - 1) * (number of column categories - 1)

= (2-1)*(3-1) = 2

Chi-square test is a right-tailed test,

So the critical value at right tail area 0.05 with DF 2 is 5.99

Decision rule:

If Chi-square test statistics > Critical value then reject the null hypothesis otherwise fail to reject the null hypothesis.

In this case test statistics(16.077) > critical value(5.99) so reject the null hypothesis.

Conclusion:

Reject the null hypothesis, that is there is an association between Anger and heart disease.