In order to shrink its labor force, a large company (such as IBM) is considering

Question

In order to shrink its labor force, a large company (such as IBM) is considering offering an early retirement package to its employees who are over fifty-five and who have been on the payroll at least ten years. However, this plan will not be cost-effective if more than 25% of such employees choose to accept this package. A random sample of 100 eligible employees indicates that 30 of them would accept the early retirement package, if it were offered. Using a 1% level of significance, test the null hypothesis that the fraction of all eligible employers who would accept the package is no greater than 0.25, against the alternative that it is greater.

Explanation / Answer

R code :

> binom.test(30,100,p=0.25,alt="g",conf.level=0.99)

Exact binomial test

data: 30 and 100
number of successes = 30, number of trials = 100, p-value = 0.1495
alternative hypothesis: true probability of success is greater than 0.25
99 percent confidence interval:
0.198316 1.000000
sample estimates:
probability of success
0.3

Since p-value > 0.01, we accept the null hypothesis and conclude that that the fraction of all eligible employers who would accept the package is not significantly greater than 0.25.

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