According to the described situation, we have that:
- The null hypothesis is
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:
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.
The test statistic is given by:
In which:
is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are:
Hence:
The value of the test statistic is of z = -0.866.
You can learn more about hypothesis tests at brainly.com/question/16313918