Can anyone help me with this?
Which of the following statements is true about a 99% confidence interval?
a. The interval contains 99% of the population.
b. The probability that the population mean is in the interval is 99%.
c. The interval is wider than a 95% confidence interval would be.
d. None of the above.
c)
When you create a 99% confidence interval this indicates that If you made many intervals by taking samples of the same size from a population then...99% of all of the intervals that you make will contain the true population mean.
It would not contain 99% of the population.
You cannot say anything about the probability of one interval that you created.
I do know that 99 is larger than 95 so you will have a wider interval.
To find the correct answer, let's break down each option and analyze them one by one:
a. The interval contains 99% of the population.
- This statement is incorrect. A confidence interval does not represent a specific percentage of the population; rather, it provides an estimate of the range in which you can say, with a certain level of confidence, that the true population parameter is likely to fall.
b. The probability that the population mean is in the interval is 99%.
- This statement is also incorrect. A confidence interval is not about the probability of the population mean being within the interval. Instead, it provides a range of values in which the population mean is likely to fall, based on a given level of confidence.
c. The interval is wider than a 95% confidence interval would be.
- This statement is correct. The width of a confidence interval is determined by the desired level of confidence. A higher confidence level requires a wider interval. Therefore, a 99% confidence interval will be wider than a 95% confidence interval.
d. None of the above.
- Since option c is true, option d, which says "none of the above," is not the correct answer.
Therefore, the correct answer is option c: The interval is wider than a 95% confidence interval would be.