SOLUTION: In a sample of 400 burners there were 12 whose internal diameters were not within tolerance Is this sufficient evidence for concluding that the manufacturing process is turning o

Question 1172326: In a sample of 400 burners there were 12 whose internal diameters were not within tolerance
Is this sufficient evidence for concluding that the manufacturing process is turning out more than
2 % defective burners. Take los to be 5%.
Found 2 solutions by Boreal, math_tutor2020:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: p=0.02
Ha: p NE 0.02
alpha=0.05 p{reject Ho|Ho true}
test is a 1 sample proportion, test stat is z and reject if |z| > 1.96
z=(0.03-0.02)/sqrt(0.02*0.98/400); the 0.03 is point estimate of 12/400
=0.01/0.007
=1.43
fail to reject Ho because of insufficient evidence to show a difference.
p-value=0.15
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The tutor Boreal has the right idea, but we're dealing with a right-tailed test since we're asking the question "is the population proportion p greater than 2 percent?", where p is the population proportion of defective burners.

We have these hypotheses
H0: p = 0.02
H1: p > 0.02
The claim is made in the alternative hypothesis.

The test statistic z = 1.43 leads to a p value of roughly 0.0764; use a table or calculator to compute this.
This means P(Z > 1.43) = 0.0764 approximately.

At level of significance (los) 5%, aka alpha = 0.05, we fail to reject the null.
We only reject the null if the p value is smaller than alpha.

The conclusion is the same as what Boreal got: There is insufficient evidence to conclude that the manufacturing process is turning out more than 2% defective burners.

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