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slavikrds [6]
2 years ago
14

The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable j

ob was available is to be investigated at the 0.02 significance level. If 74 out of the 200 workers sampled said they would return to work, what is our decision
Mathematics
1 answer:
Bad White [126]2 years ago
7 0

Answer:

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Step-by-step explanation:

Test if the proportion is less than 40%:

At the null hypothesis, we test if the proportion is of at least 0.4, that is:

H_0: p \geq 0.4

At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:

H_1: p < 0.4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

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

0.4 is tested at the null hypothesis:

This means that \mu = 0.4, \sigma = \sqrt{0.4*0.6}

74 out of the 200 workers sampled said they would return to work

This means that n = 200, X = \frac{74}{200} = 0.37

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}

z = -0.87

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.

Looking at the z-table, z = -0.87 has a p-value of 0.1922.

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

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