91影视

Let x be the number of workers who had allergies they suspected on the questionnaire.

So, x = 36

Also, the total numbers of workers are 83. That is, n = 83

Since, out of 83 workers with confirmed latex allergy, only 36 suspected that they had the allergy.

Therefore, the proportion is given as,

$$\begin{gathered} p=\frac{36}{83} \\ =0.4337 \end{gathered}$$

The confidence interval for proportion is given by,

$\mathit{p}\mathbf{卤}{\mathit{z}}_{\frac{\mathbf{伪}}{\mathbf{2}}}\mathbf{脳}\sqrt{\frac{\mathbf{p}\left(1-p\right)}{\mathbf{n}}}$

Now, from the standard normal table, the value $z_{\frac{伪}{2}}$for a 95% confidence level is 1.96.

Therefore,

$$\begin{gathered} p卤z_{\frac{伪}{2}}脳\sqrt{\frac{p\left(1-p\right)}{n}}=0.4337卤1.96脳\sqrt{\frac{0.4337\left(1-0.4337\right)}{83}} \\ =0.4337卤1.96脳\sqrt{\frac{0.4337脳0.5667}{83}} \\ =0.4337卤0.10662 \end{gathered}$$

$$\begin{gathered} =\left(0.4337-0.10662,0.4337+0.10662\right) \\ =\left(0.32712,0.54054\right) \end{gathered}$$

Therefore, it is 95% confident that the proportion of health care workers with a latex allergy suspects their allergy is between 0.32712 and 0.54011.