Final answer:
To construct a 95% confidence interval with n = 540 and p = 0.85, you calculate the margin of error using the critical value for 95% confidence, then add and subtract this margin from the sample proportion to find the lower and upper bounds of the interval.
Step-by-step explanation:
When constructing a 95% confidence interval given that n = 540 and p = 0.85, we need to calculate the margin of error and then add and subtract that margin from the sample proportion p to get the interval. To find the margin of error (EBP), we use the formula involving the critical value (Z) for the 95% confidence level, the sample proportion (p), and the sample size (n). With the TI-83, 83+, or 84+ calculator, you would input the given values for 'n' and 'p' and set the C-Level to .95 to calculate the interval.
To find the critical value Z for a 95% confidence interval, you can use the calculator function 'invNorm(0.975, 0, 1)' or look up 1.96 in the Z-table as Z0.025. Next, calculate p' (sample proportion) and q' (1 - p'), then compute EBP using the formula Z \( \sqrt{ \frac{p'(1-p')}{n} } \). The confidence interval is then p' \( \pm \) EBP.