Q.2.1 - The Practice of Statistics for AP

Question

According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. In a national survey of restaurant employees, 75% said that work stress had a negative impact on their personal lives. 11 Managers of a large restaurant chain wonder whether this national result holds for their employees. A random sample of 100 employees finds that 68 answered "Yes" when asked, "Does work stress have a negative impact on your personal life?" Is this good reason to think that the proportion of all employees in this chain who would say "Yes" differs from the national proportion of 0.75? Support your answer with a significance test.

Step-by-Step Solution

Answer

Yes the proportion of all employees in this chain who would say "Yes" differs from the national proportion of $0.75$ as there is enough evidence to support this.

Step 1: Introduction

Work pressure can be characterized as the destructive physical and close to home reactions that happen when the necessities of the gig don't match the abilities, assets, or requirements of the labourer. Work pressure can prompt chronic weakness and even injury.

Step 2: Explanation

The sample size is n = $100$

Confidence level is $95\%$

population proportion is $0.75$

Calculating the null and alternative hypotheses

$\begin{array}{r}{H}_0:p=0.75\\ H_a:p\ne 0.75\end{array}$

Using a calculator we get the p-value is larger than the significance level.

Hence, the null hypothesis is not rejected and there is enough evidence to support this.