Question

which of the following would be a correct interpretation of a 99% confidence interval such as ( 4.1<mu<5.6 )?
choose the correct answer below
a. there is a 99% chance that ( mu ) will fall between 4.1 and 5.6
b. it means that 99% of sample means fall between 4.1 and 5.6
c. it means that 99% of all data values are between 4.1 and 5.6
d. we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of ( mu )

Explanation:

• Option A: The confidence interval is not about the probability that the population parameter ($\mu$) falls in the interval. The population parameter is a fixed value, not a random variable.
• Option B: A confidence interval for the population mean ($\mu$) is not about sample means.
• Option C: A confidence interval for the population mean is not about all data values.
• Option D: By the definition of a confidence interval, if we construct many confidence intervals (at the 99% confidence level), about 99% of them will contain the True population parameter. So we are 99% confident that the interval from 4.1 to 5.6 actually does contain the True value of $\mu$.

Answer:

D. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of $\mu$