Which of the following statements correctly interprets a 95% confidence interval on a population mean?
a. It is a single point estimate
b. Used to quantify the certainty of the sample standard deviation
c. A 99% confidence interval is narrower than the 95% confidence interval
d. If we repeatedly took sample from the same population, 95% of them would contain the true population mean.
e. It is not used to interpret the population.
No idea
The correct statement that interprets a 95% confidence interval on a population mean is:
d. If we repeatedly took samples from the same population, 95% of them would contain the true population mean.
A 95% confidence interval provides a range of values within which we can be 95% confident that the true population mean lies. This means that if we were to take many samples from the same population and calculate the confidence intervals for each, approximately 95% of those intervals would contain the true population mean.
The correct answer is d. If we repeatedly took samples from the same population, 95% of them would contain the true population mean.
To understand why this is the correct answer, let's break down each statement:
a. A confidence interval is not a single point estimate. It is a range of values that is likely to contain the population parameter (in this case, the population mean).
b. A confidence interval does not quantify the certainty of the sample standard deviation. It is used to estimate the population mean, not the standard deviation.
c. A 99% confidence interval is actually wider than a 95% confidence interval. As we increase the confidence level, the interval becomes wider to account for the increased certainty required.
d. This statement correctly interprets a 95% confidence interval. It means that if we were to take repeated samples from the same population, 95% of those samples would yield confidence intervals that contain the true population mean. In other words, there is a 95% probability that the true population mean lies within the calculated interval.
e. A confidence interval is indeed used to interpret the population. It provides a plausible range of values for the population parameter based on the sample data.
So, the correct interpretation of a 95% confidence interval is that if we repeatedly took samples from the same population, 95% of them would contain the true population mean.