Question

21. A test was conducted for the significance of the difference in average education for random samples of males and females in Canada. Males received an average of 13.67 years of schooling and females received an average of 14.05 years. The obtained Z score for this difference was –59.9. Based on these results, which of the following is a reasonable conclusion?

a. The difference is important but not statistically significant. b. There is no gender gap in education in Canada. c. The difference is statistically significant. d. The difference is not statistically significant and was probably caused by random chance.

Answer 1

Answer is

c) The difference is statistically significant.

The null and alternative hypothesis is

where are mean years education for males and females

Test statistic( z score is)

the value of which is found to be

z -score = -59.9

P value is given by

P value = P( z < -59.9 ) +P( z > 59.9)

From z table , this value is almost zero

P value < 0.0001

Since P value is very small

The difference is statistically significant.