5.
What happens to the width of our confidence interval for m if we increase the sample size but keep the confidence level the same?
A)
It increases.
B)
It decreases.
C)
It stays the same.
D)
It depends on the sample mean and standard deviation.
To determine the effect of increasing the sample size on the width of the confidence interval for the population mean (m), we need to understand the relationship between sample size and confidence interval.
When calculating a confidence interval, we use a formula that involves the sample mean, standard deviation, sample size, and the desired confidence level. The width of the confidence interval is influenced by both the sample size and the confidence level.
If the sample size is increased while keeping the confidence level the same, the width of the confidence interval will decrease. This means that the range of values in which the population mean is likely to lie becomes narrower.
The reason for this is that as the sample size increases, we have more data points to estimate the population mean accurately. This reduces the variability in the estimates, leading to a narrower interval.
Therefore, the correct answer is B) It decreases. Increasing the sample size while keeping the confidence level the same will result in a narrower confidence interval for m.