Question

b) p vale ? o) ret o er fall torepeot to

Answer 1

(a)

Correct option:

H0: p1 = p2

H1: p1 > p2

(b)

$P=\frac{n1p1+n2p2}{n1+n2}$

$=\frac{(269\times 0.65)+(269\times 0.13)}{269+269}=0.39$

So,

Q = 1 - P = 0.61

$SE=\sqrt{PQ(1/n1+1/n2)}$

$=\sqrt{0.39\times 0.61(1/269+1/269)}=0.0421$

Test statistic is:

Z = (p1 - p2)/SE

= (0.65 - 0.13)/0.0421 = 12.3515

(b) Table of Area Under Standard Normal Curve gives area = 0.5 nearly.

So,

p - value = 0.5 - 0.5 nearly = 0 nearly

(c) $\alpha$ = 0.01

Since p-value is less than $\alpha$ , Reject H0.

Conclusion:
There is sufficient evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.