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Hoochie [10]
3 years ago
15

A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a randomsample of 600 disks, it is found tha

t 3% are defective, but the supplier claims that this isonly a sample fluctuation. At the 0.01 level of significance, do the data provide sufficientevidence that the percentage of defects exceeds 1%
Mathematics
1 answer:
olga55 [171]3 years ago
4 0

Answer:

At a significance level of 0.01, there is enough evidence to support the claim that the percentage of defective disks exceeds 1%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of defective disks exceeds 1%.

Then, the null and alternative hypothesis are:

H_0: \pi=0.01\\\\H_a:\pi>0.01

The significance level is 0.01.

The sample has a size n=600.

The sample proportion is p=0.03.

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.01*0.99}{600}}\\\\\\ \sigma_p=\sqrt{0.000017}=0.004

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.03-0.01-0.5/600}{0.004}=\dfrac{0.019}{0.004}=4.719

This test is a right-tailed test, so the P-value for this test is calculated as:

P-value=P(z>4.719)=0.000001

As the P-value (0.000001) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the percentage of defective disks exceeds 1%.

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