## Hypothesis Testing

2 different problems.

6. A.C. Bone has developed a duck hunting boot which they claim can remain immersed for at least 12 hours without leaking. Five hundred pairs of the boots are tested and the time until first leakage is measured. The average time until the first leakage for the sample is 12.25 hours with a standard deviation of 3 hours.

a. Find the p-value of the claim that the average time until first leakage for the hunting boot is at least 12 hours.
b. Does this sample support A.C. Bone's claim at a significance level of .01?

H0: Null hypothesis
H1: Alternative Hypothesis
Mx = Mu of x
n = sample
Sx = standard deviation

a. H0: Mx less than or equal to 12
H1: Mx greater than 12

b. alpha = .01
n = 500
Sx = 3
x bar = 12.25

Zts = (x bar - Mx) / Sx / SQRT (n)) = (12.25-12) / 3 / SQRT (500))
Zts = 1.863

Zcu = invnorm (.99, 0, 1) = 2.326

Zts = 1.863 > 2.326 = Zcu
reject H1

Is this correct?

5. A production process will normally produce defective parts 0.2&#37; of the time. In a random sample of 1,400 parts, three defectives are observed.

a. Find the p-value for testing the hypothesis that the process produces defective parts more than 0.2% of the time.
b. Is there sufficient evidence at the 0.05 level to indicate that the defective rate of the process has increased?

a. H0: p less than equal to .2
H1: p greater than .2

b. alpha = .05
n = 1400
x = 3
p hat = 3/1400 = .002

Zts = (p hat - p) / SQRT(p(1-p)/n) = (.002-.2) / SQRT(.2(1-.2) / 1400) = -18.52????

I don't think you can have a negative so either I am doing something wrong or the problem is written incorrectly.