Question

An Air Pollution Study studies the correlation between air pollution and the disease atherosclerosis. Nationally, 40% of adults suffer from atherosclerosis. It is suspected that the proportion of people with atherosclerosis in high-pollution areas is higher. In a Simple Radom Sample (SRS) of 600 residents of high-pollution areas, he finds that 270 subjects have atherosclerosis with a sample standard deviation of .02. At the 1% level (α = .01), conduct a hypothesis test whether people in high-pollution areas are more likely to have atherosclerosis?

1. What are the null and alternative hypotheses?

2. What is the value of the sample proportion (what percentage of the residents have atherosclerosis)?

3. Find the z-value and corresponding p-value

4. Is the result statistically significant, why or why not? (explain in context of your hypothesis)

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.4
Alternative Hypothesis, Ha: p > 0.4

b)

sample proportion = 270/600 = 0.40

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.45 - 0.4)/sqrt(0.4*(1-0.4)/600)
z = 2.5

P-value Approach
P-value = 0.0062

d)

As P-value < 0.01, reject the null hypothesis.