Question

testing laboratory gloves the new york times published an article about a study in which professor denise korniewicz and other johns hopkins researchers subjected laboratory gloves to stress. among 240 vinyl gloves, 63% leaked viruses. among 240 latex gloves, 7% leaked viruses. see the accompanying display of the statdisk results. using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Answer 1

To test the claim that vinyl gloves have a greater virus leak rate than latex gloves, we can perform a hypothesis test using a one-sample proportion test.

Step-by-step explanation:

To test the claim that vinyl gloves have a greater virus leak rate than latex gloves, we can perform a hypothesis test. The null hypothesis is that the virus leak rates for vinyl and latex gloves are equal, while the alternative hypothesis is that the virus leak rate for vinyl gloves is greater than for latex gloves.

We can use a one-sample proportion test to compare the leak rates. The test statistic is the z-score, which can be calculated using the formula:

z = (p1 - p2) / √((p1(1-p1)/n1) + (p2(1-p2)/n2))

where p1 and p2 are the proportions of virus leak for vinyl and latex gloves respectively, and n1 and n2 are the sample sizes.

By plugging in the given values, we can calculate the z-score and compare it to the critical value at a 0.01 significance level. If the z-score is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.