Question

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 279 vinyl gloves, 60% leaked viruses. Among 279 latex gloves, 14% leaked viruses. See the accompanying display of the technology results. Using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Identify: null, alternative hypothesis, test statistic, and P-value.

The P-value is (1) the significance level ?, so (2) the null hypothesis. There is (3) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

1) greater than / less than 2) reject / fail to reject 3) sufficient / insufficient

(Table at bottom of question)

Technology results:

Pooled proportion: 0.37

Test statistic, z: 11.3049

Critical z: 1.2816

P-value: 0.0000

80% Confidence interval: 0.4163430 < p1 ? p2 < 0.5083882

Answer 1

a) H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

The P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Explanation:

(a) From the information given, we can identify the null hypothesis and alternative hypothesis.

H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

(b) n1 which is size of sample 1 = 279

p1 which is proportion of sample 1= 0.60

n2 which is size ofsample 2 = 279

p2 which is proportion of sample 2 = 0.14

P=n1p1+n2p2 / n1+n2

=279 × 0.60+279 × 0.14/279+279

=0.37

Q = 1- P = 0.63

SE= √PQ(1/n1+1/n2)

= √ 0.37 × 0.63(1/279+1/279)=0.0409

So,

Test statistic is:

Z = (p1 - p2) /SE

= (0.60 - 0.14)/0.0409

= 11.3049

(c) The able of Area Under Standard Normal Curve gives the following area =

0.5 approximately.

So,

P-value = 0.5 - 0.5 nearly =0 nearly

(d)From the information derived, the P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.