Final answer:
To estimate a 99% confidence interval for the population mean of drug treatments without a known population standard deviation, apply the t-distribution, calculate the error bound, and construct the interval using the sample mean plus or minus the error bound.
Step-by-step explanation:
To find a 99% confidence interval estimate of the population mean with drug treatments, you should follow these steps:
- Find the point estimate for the population mean. This is usually the sample mean of your data.
- Since the population standard deviation is unknown, you must apply the t-distribution.
- Define the random variable X as the mean effective length of time of the drug treatment.
- Calculate the sample standard deviation if it's not provided.
- Determine the degrees of freedom (df), which is the sample size minus one, n-1.
- Use a t-table to find the t-value that corresponds to a 99% confidence level with your df.
- Calculate the error bound using the t-value, sample standard deviation, and the square root of the sample size.
- Finally, construct the confidence interval by adding and subtracting the error bound from the sample mean.
Interpreting a 99% confidence interval means that if you were to take many samples and calculate an interval in the same way, 99% of the intervals would contain the true population mean.