A work-sampling study resulted in 270 successes in 350 trials. A 95% two-sided confidence interval for the proportion of successes in this study is most nearly:

To calculate the 95% two-sided confidence interval for the proportion of successes in the work-sampling study, we first determine the sample proportion (p-hat) of successes. This is obtained by dividing the number of successes by the total number of trials. In this case:

[ p\hat = \frac{270}{350} = 0.7714 ]

Next, we need to calculate the standard error (SE) of the sample proportion. The standard error for a proportion is given by the formula:

[ SE = \sqrt{\frac{p\hat (1 - p\hat)}{n}} ]

Where ( n ) is the number of trials. Substituting the values we have:

[ SE = \sqrt{\frac{0.7714 \times (1 - 0.7714)}{350}} ]

Calculating ( 1 - p\hat ):

[ 1 - 0.7714 = 0.2286 ]

Now we calculate the standard error:

[ SE = \sqrt{\frac{0.7714 \times 0.2286}{350}} = \sqrt{\frac{0.1766}{350}} = \sqrt{0