Question

A manufacturer claims that only 1% of their computers are defective, but in a sample of 600 3% were found to be defective. If the 1% claim were true there would be less than 1 chance in 1000 of getting this number of defects in the sample. Is there statistically significant evidence against the manufacturer's claim? Why or why not?

No, because the difference between a 1% and a 3% defect rate is insignificant.

Yes, because the source of the data was unbiased.

Yes, because the results are unlikely to occur by chance.

No, because the sample size was too small to reach a conclusion.

Answer 1

Yes, because the results are unlikely to occur by chance.

Explanation:

We have to remember that when dealing with statistics the larger the sample we are taking, the more the results will tend to the statistical reality, for example, if we flip a coin, the chances or statistics are 50%-50% but if we only toss it two times, theres a singnificant chance that it could be 100% tails, the more we continue to toss the coin, the closer we will get to the 50-50, here we have a really large sample of 600 computers, where 3% of them were defective, so we can assure that it wasn´t by chance, because an increase of 2% on the percetange of the defective devices from the ideal to the reality is not by chance.

Answer 2

Explanation:

Here population parameter p= 1% = 0.01

But sample proportion = 0.03

Sample size = n=600

Std error of the sample =
`\sqrt{(pq)/(n) } =\sqrt{(0.1(0.9))/(600) } \\=0.01225\\`

Let us assume significance level as 5%

For proportion z critical for 95% is 1.96

Margin of error = 1.96(std error) = 0.024

Conf interval for proportion lower bound = 0.01-0.024 =- 0.014

Upper bound = 0.01+0.024 = 0.124

Thus conf interval (-0.014, 0.124)

Our sample proportion is 0.03 which does not lie within this interval.

Hence we conclude that

Yes, because the results are unlikely to occur by chance.