Question

Warren works for the Air Pollution Study at the University of Houston, and studies the correlation between air pollution and the disease atherosclerosis. Nationally, 40% of adults suffer from atherosclerosis. Warren suspects that the proportion of people with atherosclerosis in high-pollution areas is higher. In a SRS of 300 residents of high-pollution areas, he finds that 140 subjects have atherosclerosis. At the 1% significance level, is this good evidence that people in high-pollution areas are more likely to have atherosclerosis?

Part a: What are the null and alternative hypothesis for this study?

Part b: Sketch the reject region.

Part c: Calculate the test statistic. Plot this value in your sketch in part b.

Part d: Determine the P-value for your test.

Part e: State your conclusion clearly in complete sentences. Make sure to phrase your conclusion in terms of the scientific question of interest (saying that you reject or fail to reject is not enough).

Answer 1

Given Population Proportion = P = 40% 0.4

Given Sample Size = n = 300 ( Large Sample )

Given x = 140

We know that

We know that

(a) Hypothesis:

The people in high-pollution areas are more likely to have atherosclerosis

The people in high-pollution areas are not more likely to have atherosclerosis

(b) Rejection Region:

Given

Therfore

(c) To test the we use the Z - Statistic

Difference between sample and population proportions:

Standard Error of p :

Therefore

(d) p - value:

The P-Value is 0.018428 i.e 0.02

The result is not significant at p < 0.01

· If the p-value ≤ α, we reject the null hypothesis in favour of the alternative hypothesis.

· If the p-value > α, we fail to reject the null hypothesis. We do not have enough evidence to support the alternative hypothesis.

(e)

Since p - value > alpha i.e 0.02 > 0.01; So, we fail to Reject

Therefore we conlcude that "The people in high-pollution areas are more likely to have atherosclerosis".

Using the Below posted Standard Normal tabulated valued we drawn the Z value.