## A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of

Question

A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer’s claim based on this observation?

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3 years 2021-08-11T17:51:46+00:00 1 Answers 12 views 0

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer’s claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that

Value of the test statistic:

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 – 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer’s claim based on this observation.