Question

Assignment 9B

There have been many studies that looked at the incidence of heart attack on the different days of the week. Studies in Japan and Scotland seemed to find that there was a substantial “spike” in heart attacks on Mondays, perhaps as many as 20% more. A researcher studied a random selection of 200 heart attack victims and recorded the day of the week that their attack occurred. The following table summarizes the results:

Day	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Count	24	36	27	26	32	26	29

The researcher was interested in whether the distribution of heart attacks was the same or different across the days of the week.

1. What are the null and alternative hypotheses the researcher should establish?

2. Under the appropriate null hypothesis, what is the expected number of heart attacks that occur on Monday?

3. Find the test statistic for the data. Give its degrees of freedom.

4. Which day contributes most to the chi-square statistic? How large is this contribution?

5. Assuming a significance level of .05, make a decision and write a conclusion.

Answer 1

Day	Observed Frequency	Ei = 200/7	(Oi - Ei)^2/Ei
Sunday	24	28.5714	0.7314
Monday	36	28.5714	1.9314
Tuesday	27	28.5714	0.0864
Wednesday	26	28.5714	0.2314
Thusday	32	28.5714	0.4114
Friday	26	28.5714	0.2314
Saturday	29	28.5714	0.0064
			3.6300

H0: The number of heart attacks across different days in a week follow uniform distribution
Ha: The number of heart attacks across different days in a week do not follow uniform distribution

on monday expected number of heart attacks are 28.5714

test statistic, chi-square = 3.63

df = 6

Monday contributes the most
36 - 28.5714 = 7.4286

p-value = 0.7266
As p-value > 0.05, fail to reject H0
There are not significant evidence to conclude that The number of heart attacks across different days in a week do not follow uniform distribution