Question

Is there a significant difference in the level of community service participation between college and high school graduates? According to the GSS 2014, 44% of 88 college graduates reported volunteering in the previous month compared with 30% of 245 high school graduates. What is the research hypothesis? Should you conduct a one- or a two-tailed test? Why? Present the five-step model, testing your hypothesis at the .05 level. What do you conclude?

Answer 1

As we are trying to test whether the proportion of college graduates who volunteer and the proportion of school graduates who volunteer are different, therefore the null and the alternative hypothesis here are given as:

As we are testing it from both sides, this is a two tailed test.

Now the pooled proportion here is computed here as:

The standard error here is computed as:

Now the test statistic here is computed as:

As this is a two tailed test, the p-value here is computed from the standard normal tables as:

p = 2P( Z > 2.3832 ) = 2*0.0086 = 0.0172

As the p-value here is 0.0172 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here and conclude that we have sufficient evidence that there is a significant difference in the level of community service participation between college and high school graduates.