Final answer:
To construct a 99% confidence interval for the proportion of patients who did not have at least one clergy visit, calculate the sample proportion and standard error, then add and subtract the margin of error from the sample proportion.
Step-by-step explanation:
To construct a confidence interval for the proportion of patients who did not have at least one clergy visit, we first need to calculate the sample proportion.
The sample proportion is calculated by subtracting the number of patients who had at least one clergy visit from the total number of patients surveyed, and then dividing by the total number of patients surveyed. In this case, the sample proportion is (806 - 492) / 806 = 0.388.
Next, we need to calculate the standard error, which is given by the formula sqrt((p * (1 - p)) / n), where p is the sample proportion and n is the sample size.
Plugging in the values, we get sqrt((0.388 * (1 - 0.388)) / 806) = 0.021.
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the sample proportion.
The margin of error is calculated by multiplying the standard error by the appropriate z-score for the desired confidence level.
The z-score for a 99% confidence level is approximately 2.576.
Plugging in the values, the margin of error is 2.576 * 0.021 = 0.054.
Therefore, the 99% confidence interval for the proportion of patients who did not have at least one clergy visit is 0.388 ± 0.054, or (0.334, 0.442).