In August 2003, 56% of employed adults in the United States reported that basic
ID: 2956023 • Letter: I
Question
In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the placement office at a 4-year college thinks this percentage has increased due to increased use of technology in the workplace. He takes a random sample of 480 employed adults and finds that 297 of them feel that basic mathematical skills are critical or very important to their job. Is there sufficient evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased at the a = 0.05 level of significance?Explanation / Answer
First, suppose that nothing has changed, and possibility p is still 0.56. It's our null hypothesis. Now, we've got Bernoulli distribution, but 480 is big enough to consider Gaussian distribution instead. It has mean 480*0.56=268.8 and its standard deviation is sqrt(480*0.56*(1-0.56))=10.88 (I hope you saw formulas like s=v(npq)) So 297 is (297-268.8)/10.88 = 2.59 stds above the mean. So the level increased with a ˜ 0.005 level of significance, and there is sufficient evidence.