[zetablue1]

I have been given a earnings data set and I need to set up a research hypothesis. I have an idea but I am not sure if it is sound.

My research question is: Does education affect an individual's earning potential?

The data set information includes:
annual wage, occupation, education, race, gender, marital status, age, and if union affiliated.

My thought was to hypothesize that people with more than a high school education earn at least $10,000 more per year at α=.025. According to the data set 101 people were surveyed the sample mean for earnings is $30,833 with a sample standard deviation of $16,947. Forty people had higher than a high school education. T = 1.984

Ho: ≤ people with less education earn less
Ha: > people with more education earn more

Reject Ho if t > 1.984

30,833-10,000/16,947/√101= 12.35

I am not really sure if this is on the right track. I have never had to set up a research hypothesis... please guide me in the right direction.

[morgaine300]

Well, straight off the top I can't answer your question, but so far no one else has touched it so... Whenever we did this type of thing (it was actually an opinion on some political issue or other, but based on the same sorts of demographics), I think we set up a joint probability table and conditional probabilities, and were not doing hypothesis testing of the sort you are doing.

What I can do is tell you the part that you're doing wrong. You're mixing up two sets of data. One is the salaries of all people surveyed, but then you're mixing into, on the same x line, only those who have higher than a high school education. Your x line is all the people surveyed because you're using data from the entire survey.

Working out the math, the only thing you've shown is the z score for ANYONE earning greater than 10,000. There isn't anything in there that accounts for the people having higher than a high school education. Do you see what I mean?

Ho and Ha have to be about earning more or less than something. What's the "something."?

I'm not sure, but I think you need to be maybe comparing a sample of +high school to the average of no more than high school, and see if it's actually 10,000 higher?

Also note that "10,000 higher" is actually not the 10,000 at the left side -- you're saying higher than people with no more that higher school. Somehow you've got to split these people up to compare them. i.e. what's average for no more than high school compared to more than high school? Earning $10,000 isn't the same as earning "10,000 more than something else."

That's not really totally an answer, but may help you get off thinking the right direction.

[zetablue1]

Well, straight off the top I can't answer your question, but so far no one else has touched it so... Whenever we did this type of thing (it was actually an opinion on some political issue or other, but based on the same sorts of demographics), I think we set up a joint probability table and conditional probabilities, and were not doing hypothesis testing of the sort you are doing.

What I can do is tell you the part that you're doing wrong. You're mixing up two sets of data. One is the salaries of all people surveyed, but then you're mixing into, on the same x line, only those who have higher than a high school education. Your x line is all the people surveyed because you're using data from the entire survey.

Working out the math, the only thing you've shown is the z score for ANYONE earning greater than 10,000. There isn't anything in there that accounts for the people having higher than a high school education. Do you see what I mean?

Ho and Ha have to be about earning more or less than something. What's the "something."?

I'm not sure, but I think you need to be maybe comparing a sample of +high school to the average of no more than high school, and see if it's actually 10,000 higher?

Also note that "10,000 higher" is actually not the 10,000 at the left side -- you're saying higher than people with no more that higher school. Somehow you've got to split these people up to compare them. i.e. what's average for no more than high school compared to more than high school? Earning $10,000 isn't the same as earning "10,000 more than something else."

That's not really totally an answer, but may help you get off thinking the right direction.

Ok. Actually that did help. I changed my hypothesis to compare the national average salary (Ho: ≤ to the national average) and the average salary of the people, in my sample with more than 12 years of experience (Ha > the national average). The national average is 30,833 with a standard deviation of 16,947. Out of the 100 people surveyed 39 had higher than 12 years of education and earned a total of 1,536432. At the .05 significance level is the mean salary for this group greater than the national average?

Thank you. I am pretty sure about the correct formula to use for the calculation but I just wasn't sure if I had a sound hypothesis or if I am plugging the numbers in correctly.

Reject Ho if z > 1.645

30,833-35,396/16,947/√39 = 1.681
Reject Ho at .05
p value = 1-.9537= .0464, reject Ho because p value is smaller than .05