What effect will an outlier have on a confidence interval that is based on a small sample size?
A) The interval will be smaller than an interval without the outlier.
B) The interval will be the same with or without the outlier.
C) The confidence interval will be wider than an interval without the outlier.
D) The interval will reveal exclusionary data.
C.I. for mu = x +/- z*sigma.
Look at c.
What effect will an outlier have on a confidence interval that is based on a small sample size?
C) The confidence interval will be wider than an interval without the outlier.
The correct answer is C) The confidence interval will be wider than an interval without the outlier.
When calculating a confidence interval, we use statistical methods to estimate the range within which the true population parameter is likely to fall. This estimate is based on the data from a sample.
An outlier is a value that is significantly different from the other values in the data set. When an outlier is present in a small sample, it can have a substantial impact on the average and standard deviation of the data. As a result, including an outlier in the calculation of a confidence interval will lead to a larger standard deviation, which in turn leads to a wider confidence interval.
In other words, the outlier influences the variability of the data, making it more spread out. This increased spread affects the width of the confidence interval, indicating a higher level of uncertainty in our estimation.
Therefore, the presence of an outlier in a confidence interval based on a small sample size will result in a wider interval compared to an interval calculated without the outlier.