Question

A new method of HIV testing has been proposed based on a new quick detection procedure where saliva is examined. Suppose that the new method tests 867 persons and falsely categorizes 25 of the 176 HIV positive results. Assuming the current best standard of practice for saliva based quick detection HIV tests has a false positive rate of only 10%, determine if the efficacy of the two tests are significantly different. Write out your null and alternative hypotheses and interpret your results and use an alpha level of 0.05. Is a normal approximation appropriate? Why or why not?

		Yes, npq>5 Ho: p=.10, Ha: p≠0.10 Z statistic=1.8573, pvalue of 0.0633 Fail to reject the null hypothesis that the failure rate in the new detection mechanism is any better than the current system.
		No, npq<5 Ho: p=.10, Ha: p≠0.10 Z statistic=1.7771, pvalue of 0.0006 Fail to reject the null hypothesis that the failure rate in the new detection mechanism is any better than the current system.
		Yes, npq>5 Ho: p=0.01, Ha: p≠0.010 Z statistic=2.1003, pvalue of 0.05 Reject the null hypothesis that the failure rate in the new detection mechanism is any better than the current system.

Answer 1

Answer:

Yes, npq>5

Ho: p=.10, Ha: p≠0.10

Z statistic=1.8573, p-value of 0.0633

Fail to reject the null hypothesis that the failure rate in the new detection mechanism is any better than the current system.

Explanation:

To test whether there is a significant difference in results from the survey for the new quick detection procedure, the z test for the one proportion is used (the sample data values satisfy the normality condition )

Hypothesis

The null and alternative hypotheses are defined as,

This is a two-tailed test/

The significance level = 0.05

Test statistic

The z-statistic is obtained using the formula,

The p-value is obtained from z-distribution table for z = 1.859

Since the P-value is 0.063>0.05 at a 5% significant level, the null hypothesis is not rejected. Hence there is not sufficient evidence that the failure rate in the new detection mechanism is any better than the current system.