Question

A business magazine conducted a survey of 751 employees who had been at their current employer for 5 or more years. Of these employees, 295 responded that they were bored in their current position. Create a 99% confidence interval for the proportion of employees who have been with their current employer for 5 or more years and reported being bored in their current position. Use Excel to create the confidence interval, rounding to four decimal places.

Answer 1

the
`95\%` confidence interval for the population proportion is:

`\left [0.3469, \hspace{0.1cm} 0.4387\right]`

Explanation:

To solve this problem, a confidence interval of
`(1-\alpha) * 100\%` for the population proportion will be calculated.

`$$Sample proportion: $\bar P=0.3928$\\Sample size $n=751$\\Confidence level $(1-\alpha)*100\%=99\%$\\$\alpha: \alpha=0.01$\\Z values (for a 99\% confidence) $Z_(\alpha/2)=Z_(0.005)=2.5758$\\\\Then, the (1-\alpha) * 100\%$ confidence interval for the population proportion is given by:\\\\\left [\bar P - Z_{(\alpha)/(2)}\sqrt{(\bar P(1- \bar P))/(n)}, \hspace{0.3cm}\bar P + Z_{(\alpha)/(2)}\sqrt(\bar P(1- \bar P))/(n) \right ]`

Thus, the
`95\%` confidence interval for the population proportion is:

`\left [0.3928 - 2.5758\sqrt{(0.3928(1-0.3928))/(751)}, \hspace{0.1cm}0.3928 + 2.5758\sqrt{(0.3928(1-0.3928))/(751)} \right ]=\left [0.3469, \hspace{0.1cm} 0.4387\right]`