The manufacture of textile assumes that the proportion of or

zagonek34

zagonek34

Answered question

2021-12-10

The manufacture of textile assumes that the proportion of orders for late delivery of raw material is p=0.7. If at most 4 arrived late for a random sample of 12, reject the hypothesis that p=0.7 in favor of the alternative hypothesis that p<0.7. Use the binomial distribution.
a.) Find the probability of committing a type I error if the true proportion is 0.7.
b.) Find the probability of committing a type II error for the alternative p=0.6.

Answer & Explanation

xandir307dc

xandir307dc

Beginner2021-12-11Added 35 answers

Step 1
(a) To determine the probability of committing a type I error if the true proportion is 0.7 determine P(X4).
P(X4)=x=0412Cx(0.7)x(10.7)12x
=12C0(0.7)0(10.7)120+12C1(0.7)1(10.7)121
+12C2(0.7)2(10.7)122+12C3(0.7)3(10.7)123
+12C4(0.7)4(10.7)124
=0.00948
Therefore the probability of committing a type I error if the true proportion is 0.7 is 0.00948.
Step 2
(b) To determine the probability of committing a type I error if the true proportion is 0.7 determine P(X>4).
P(X>4)=x=41212Cx(0.6)x(10.6)12x
=0.9847
Therefore the probability of committing a type II error for the alternative p=0.6is0.9847.
aquariump9

aquariump9

Beginner2021-12-12Added 40 answers

Step 1
Part (a)
Given that,
n=12
p=0.7
q=0.3
Calculate the probability of committing a Type 1 error.
P(X4)=x=0412Cx0.7x0.312x
=0.000001+0.0000148+0.000191+0.00148+0.00779
=0.00947
Therefore, the probability is 0.00947.
Step 2
Part (b)
Given that,
n=12
p=0.6
q=0.4
Calculate the probability of committing Type 11 error.
P(X>4)=P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)
=0.042+0.101+0.176+0.227+0.213+0.142+0.064+0.017+0.0022
=0.9847
Thus, the probability is 0.9847.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?