A teacher wanted to know how well the gifted students in her class perform relative to her other classes. She administers a standardized test with a mean of 55 points and standard deviation of 10...

A teacher wanted to know how well the gifted students in her class perform relative to her other classes. She administers a standardized test with a mean of 55 points and standard deviation of 10 points. Her class of 31 students has an average score of 50. Test if this new sample mean has statistical significance at the 95 % confidence level.

Testing for significance we use the two-tailed results since we are only interested if the means are different, not if one is larger or smaller than the other.

• The p-value of 0.005(B11) is smaller than the alpha value of 0.05 (B8). Therefore these results are statistically significant.

• The z-critical value of 1.96 (B12) is less than the z-calculated ABS (2.78) (B7) which also reinforces that these results are statistically significant. Remember when doing this test you need to work with absolute values.

The teacher can use this statistically significant data to show that the gifted students in her class perform differently from her other classes. The difference in the standardized test means is real at the 95 % confidence level. If you wanted to know if they performed better or worse you would need to redefine the problem that way and use the one-tailed test.