Question

An executive believes that no more than 81% of the company’s employees take all of their vacation days. In a sample of 202 members, 139 employees took all of their vacation days. When testing the executive's hypothesis (using a 1% level of significance), what is the test statistic?

Answer 1

Solution: The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

  

Therefore, the test statistic is

Now we need to find the p-value. Using the standard normal table, we have:

Since the p-value is less than the significance level 0.01, we, therefore, reject the null hypothesis and conclude there is not sufficient evidence to reject the claim that no more than 81% of the company's employees take all of their vacation days.