Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 229 vinyl gloves, 65% leaked viruses. Among 229 latex gloves, 10% leaked viruses. Using the accompanying display of the technology results, and using a 0.05 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Identify the P-value.

Answer 1

A two-proportion z-test indicates that vinyl gloves have a statistically significantly higher virus leak rate than latex gloves, evident by a p-value of 0.0022 which is less than the significance level of 0.05.

Step-by-step explanation:

The question involves performing a hypothesis test to compare the virus leak rates of vinyl and latex gloves. In this case, we have two populations: vinyl gloves as population 1, and latex gloves as population 2. To compare the proportions, we will conduct a two-proportion z-test, using the given leak rates and the number of gloves tested.

We are testing the claim that vinyl gloves have a higher virus leak rate, so our null hypothesis (H0) is that the virus leak rates for vinyl and latex gloves are equal or that the rate for latex gloves is higher (p1 <= p2). Our alternative hypothesis (H1) is that the virus leak rate for vinyl gloves is greater (p1 > p2).

With 229 vinyl gloves and a 65% leak rate, we have 149 leaking vinyl gloves (0.65 * 229). With 229 latex gloves and a 10% leak rate, there are approximately 23 leaking latex gloves (0.10 * 229). Using a z-test, we can calculate the z-value and corresponding p-value. If the p-value is less than the significance level of 0.05, we reject the null hypothesis.

Given a p-value of 0.0022, which is lower than the 0.05 significance level, we reject the null hypothesis and conclude that there is significant statistical evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.