Material safety data sheets. The Occupational Safety &Health Administration has required companies that handle hazardous chemicals to complete material safety datasheets (MSDSs). These MSDSs have been criticized for being too hard to understand and complete by workers. A

study of 150 MSDSs revealed that only 11% were satisfactorily completed (Chemical & Engineering News, February7, 2005).

a. Give a point estimate of p, the true proportion of MSDSs that are satisfactorily completed.

b. Find a 95% confidence interval for p.

c. Give a practical interpretation of the interval, part b.

It is given that the survey conducted on Material Safety Data (MSD) by The Occupational Safety & Health Administration, is found to be tough to comprehend by the workers. Out of 150 MSDs, only 11% had been completed.

a.

Here, MSDs stand for Material Safety Data. Therefore, the true proportion of MSDs that are satisfactorily completed is denoted by the point estimate . This value in question is given to be 11%.

Therefore, $\hat{p}=0.11$.

The 95% confidence interval for proportion ‘p’ is denoted by the formula:

$CI=\hat{p}\pm z\sqrt{\frac{\hat{p}\left(1-\right)}{n}}$

Now, $=0.11,\left(1-\right)=0.89andn=150$. Also, z value for 95% level of significance is $\pm 1.96$.

Substituting we get,

$$\begin{gathered} CI=0.11\pm 1.96\sqrt{\frac{0.11\times 0.89}{150}} \\ =0.11\pm 0.05 \end{gathered}$$

Therefore, the confidence interval is $\left(0.06,0.16\right)$.

c.

The interval$0.11\pm 0.05$encloses an unknown population parameter with a certain level of confidence that is 95%. This means that one can 95% confident that true value of population proportion lies in the interval$\left(0.06,0.16\right)$ .