# Thread: solving a statistic problem using significance level of 0.05

1. ## solving a statistic problem using significance level of 0.05

A manufacturer finds that in a random sample of 100 of its tvs, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nodefective tvs and is prepared to exaggerate. What is the highest rate of nondefective tvs that the manufacturer could claim in the following condition?
His claim would not be rejected at the 0.05 significant level if this sample data were used. Assume that a left tailed hypothesis test would be used.

a.)98.4%
b.)96.5%
c.)96.6%
d.)98.2%

2. Originally Posted by tennisair
A manufacturer finds that in a random sample of 100 of its tvs, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nodefective tvs and is prepared to exaggerate. What is the highest rate of nondefective tvs that the manufacturer could claim in the following condition?
His claim would not be rejected at the 0.05 significant level if this sample data were used. Assume that a left tailed hypothesis test would be used.

a.)98.4%
b.)96.5%
c.)96.6%
d.)98.2%
It looks to me like the manufacturer can exaggerate to a greater extent than the above options allow .... Since n is large:

$\Pr\left( p < \hat{p} + 1.64 \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \right) = 0.95$

where in your problem $\hat{p} = 0.96$ and $n = 100$.

3. ## clarification

so the answer is 96.5% or 96.6%?

Restored edit by OP: so I plugged p and n into the equation you posted..but I didn't get any of the multiple choice solutions. did i do this right.? i actually got .050949..would I subtract that from 100 to get the highest rate of percent?

4. So what is the final outcome to this?

5. Originally Posted by jmsal
So what is the final outcome to this?
If more help is needed please say what part of my first reply needs further explanation.

6. I was referring to the answer.