Answer:
Explanation:
To test the claim that vinyl gloves have a greater virus leak rate than latex gloves, we can use a two-sample proportion z-test. The null hypothesis is that the proportion of vinyl gloves that leak viruses is equal to the proportion of latex gloves that leak viruses. The alternative hypothesis is that the proportion of vinyl gloves that leak viruses is greater than the proportion of latex gloves that leak viruses.
Let p1 be the proportion of vinyl gloves that leak viruses, p2 be the proportion of latex gloves that leak viruses, n1 be the sample size of vinyl gloves, and n2 be the sample size of latex gloves.
The test statistic is calculated as:
z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))
where p = (x1 + x2) / (n1 + n2) is the pooled proportion of gloves that leaked viruses, and x1 and x2 are the number of gloves that leaked viruses in each sample.
Using the data given in the problem, we have:
p1 = 0.61, n1 = 210
p2 = 0.08, n2 = 210
p = (x1 + x2) / (n1 + n2) = (0.61210 + 0.08210) / (210 + 210) = 0.345
z = (0.61 - 0.08) / sqrt(0.345*(1-0.345)*(1/210 + 1/210)) = 9.41
The critical value for a one-tailed test at a significance level of 0.05 is 1.645. Since our test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Therefore, we can conclude that there is a significant difference between the virus leak rate of vinyl gloves and latex gloves, and vinyl gloves have a higher virus leak rate compared to latex gloves.