Question

In a certain population of at risk patients, 5.2% ultimately die of a cardiovascular event in a five year window. A new medicine is developed with the hope of reducing the rate of death due to a cardiovascular event. A random sample of 2000 people from the population of at risk patients was taken and given the new medicine for five years. It was found that 82 of them died from a cardiovascular event. Is there evidence that the new medicine is effective in reducing the proportion of cardiovascular deaths? Perform a Hypothesis Test.

1. Describe the population. 2. Describe the sample. 3. Give the null and alternative hypotheses for determining whether or not the new medicine is effective in reducing the proportion of cardiovascular deaths 4. Verify the conditions. 5. Determine the sampling distribution of ˆp if the null hypothesis is true. 1 6. Calculate the value of the z-test statistic. 7. Determine the p-value for the hypothesis test. 8. Use your p-value to assess the strength of evidence against the null hypothesis. 9. Write a final statement in terms of the alternative hypothesis.

Answer 1

1: Population: Percentage of risk patients that ultimately die of a cardiovascular event in a five year window.

2. Sample: A random sample of 2000 people from the population of at risk patients and given the new medicine for five years.

3. Null and Alternative hypothesis:

Ho : p = 0.052

H1 : p < 0.052

4. Condition:

The data are a simple random sample from the population of interest.

The Sample size is large enough.

n⋅p≥10 and n⋅(1−p)≥10 , where n is the sample size and p is the true population proportion.

5. n = 2000, x = 82

p̄ = x/n = 0.041

6. Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.041 - 0.052)/√(0.052 * 0.948/2000) = -2.2157

7. p-value = NORM.S.DIST(-2.2157, 1) = 0.0134

8. The p-value is no very strong against the null hypothesis.

9. p-value < α, Reject the null hypothesis

There is enough evidence to conclude that the new medicine is effective in reducing the proportion of cardiovascular deaths.