Question

Two groups of data have different means but the same standard deviations. What is the minimum number of standard deviations that would need to separate the two means in order for the means to be considered significantly different? Assume that a is set at 5%.

-4 standard deviations.
-3 standard deviations.
-2 standard deviations.
-1 standard deviation.

Answer 1

At least -2 standard deviations are required to separate two means for them to be considered significantly different at a 5% significance level.

Step-by-step explanation:

To determine the minimum number of standard deviations that would need to separate two means for them to be considered significantly different with a 5% significance level, we use the concept of z-scores in hypothesis testing. Commonly, a z-score of approximately 1.96 (or about 2 standard deviations) in either direction is considered the cutoff for significance at the 5% level in a two-tailed test. This corresponds to a 2.5% chance in each tail of the normal distribution. Therefore, out of the options provided, at least -2 standard deviations is the minimum required for the means to be significantly different at the 5% level.