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balandron [24]
2 years ago
15

This claim is to be investigated at .01 levels. “Forty percent or more of those persons who retired from an industrial job befor

e the age of 60 would return to work if a suitable job were available. “Seventy-four persons out of the 200 sampled said they would return to work
- State the null hypothesis.
- What is the decision rule?
- Compute the value of the test statistic.​
Mathematics
1 answer:
Degger [83]2 years ago
7 0

According to the described situation, we have that:

  • The null hypothesis is H_0: p < 0.4

The decision rule is:

  • z < 2.327: Do not reject the null hypothesis.
  • z > 2.327: Reject the null hypothesis.

The value of the test statistic is of z = -0.866.

<h3>What is the null hypothesis?</h3>

The claim is:

"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"

At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:

H_0: p < 0.4

<h3>What is the decision rule?</h3>

We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.

Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:

  • z < 2.327: Do not reject the null hypothesis.
  • z > 2.327: Reject the null hypothesis.

<h3>What is the test statistic?</h3>

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

  • \overline{p} is the sample proportion.
  • p is the proportion tested at the null hypothesis.
  • n is the sample size.

In this problem, the parameters are:

p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37

Hence:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

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

z = -0.866

The value of the test statistic is of z = -0.866.

You can learn more about hypothesis tests at brainly.com/question/16313918

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