Can you please help with this question. The only thing that I have come up thus far is that I am using the z critical value because I am estimating a population proportion. Am I on the right track?
An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were latter dropped or dismissed (based on data from the Physician Insurers Association of America).
Use the formulas to construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed. Round the point estimate and the interval limits to the nearest thousandth. Use the rounded value of the point estimate when computing your interval limits. Make sure you also state the critical value that is used to find the interval limits and interpret your interval with an appropriate statement.
You can use a proportional confidence interval formula for large samples.
Here's one:
CI99 = p + or - (2.58)[√(pq/n)]
...where p = x/n; q = 1 - p; + or - 2.58 represents the 99% confidence interval using a z-table.
Substituting into the formula, we have this:
CI99 = 856/1228 + or - (2.58)[√(856/1228)(372/1228)/1228]
Convert fractions to decimals. This will make your calculations easier to do.
I hope this will help get you started.
Yes, you are on the right track. To construct a confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed, you can use the z critical value because you are estimating a population proportion.
Here's how you can proceed:
1. Calculate the point estimate: The point estimate is the sample proportion. In this case, the point estimate is calculated as the number of dropped or dismissed lawsuits divided by the total number of lawsuits: 856/1228.
2. Calculate the standard error: The standard error is calculated as the square root of (p-hat * (1 - p-hat) / n), where p-hat is the point estimate and n is the sample size. In this case, p-hat is the point estimate calculated in step 1, and n is 1228.
3. Find the z critical value: Since you want to construct a 99% confidence interval, you need to find the z critical value that corresponds to a 99% confidence level. This critical value can be obtained from the standard normal distribution table or using a statistical software. For a 99% confidence level, the z critical value is approximately 2.576.
4. Calculate the margin of error: The margin of error is calculated as the product of the z critical value and the standard error: z_critical * standard_error.
5. Calculate the confidence interval: Subtract the margin of error from the point estimate to get the lower limit of the confidence interval, and add the margin of error to the point estimate to get the upper limit of the confidence interval.
6. Round the point estimate and the interval limits to the nearest thousandth.
7. State the critical value used to find the interval limits: In this case, you can state that a z critical value of 2.576 was used to find the interval limits.
8. Interpret the interval: Finally, you can interpret the interval by saying something like: "With 99% confidence, we estimate that the proportion of medical malpractice lawsuits that are dropped or dismissed is between [lower limit] and [upper limit], rounded to the nearest thousandth."
By following these steps, you should be able to construct a 99% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed.