Question

a newspaper published an article about a study in which researchers subjected laboratory gloves to stress. among 254 vinyl gloves, 62% leaked viruses. among 254 latex gloves, 6% 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.
what are the null and alternative hypotheses?
a ( h_0: p_1 = p_2 ), ( h_1: p_1
eq p_2 )
b ( h_0: p_1 > p_2 ), ( h_1: p_1 = p_2 )
c ( h_0: p_1 = p_2 ), ( h_1: p_1 > p_2 )
d ( h_0: p_1
eq p_2 ), ( h_1: p_1 = p_2 )
e ( h_0: p_1 < p_2 ), ( h_1: p_1 = p_2 )
f ( h_0: p_1 = p_2 ), ( h_1: p_1 < p_2 )
identify the test statistic
13.31 (round to two decimal places as needed.)
identify the p - value
(round to three decimal places as needed.)

Explanation:

The problem is about testing a claim regarding the virus leak rate of vinyl gloves (population 1) and latex gloves (population 2). The null hypothesis \(H_0\) typically assumes no difference (equality), and the alternative hypothesis \(H_1\) reflects the claim. The claim is that vinyl gloves have a greater virus leak rate than latex gloves, so \(H_0: p_1 = p_2\) and \(H_1: p_1 > p_2\), which corresponds to option C.

Answer:

C. \(H_0: p_1 = p_2\), \(H_1: p_1 > p_2\)