Question

The math department is trying to determine if their tests have a gender bias. They look at scores at old exams which were normally distributed and take a random sample of students. They found that the scores of the 16 male students had a normal distribution with a mean of 73.4 and a standard deviation of 6.8. The scores of the 17 females students had a normal distribution with a mean of 77.4 and a standard deviation of 6.2. Using a significance level of 0.05, test the claim the tests have a gender bias.

Answer 1

We are to test whether there is a gender bias, therefore we are testing here whether the 2 means are equal. Therefore the null and the alternate hypothesis here are given as:

The standard error here is computed as:

The test statistic for testing the difference in means is computed here as:

For n1 + n2 - 2 = 16 + 17 - 2 = 31 degrees of freedom, we get from the t distribution tables:

p = P( t31 < -1.7624) = 0.0439

As the p-value here is 0.0439 < 0.05 that is the level of significance, the test is significant and we can conclude that we have sufficient evidence that there is gender bias.