Forming a null and alternative hypothesis and then testing it.

#1
I am given the following data:

Observation Wage
1 $8.75
2 $10.00
3 $10.25
4 $6.50
5 $15.00
6 $10.00
7 $8.00
8 $7.50
9 $12.75
10 $9.25

From this I get a sample mean of 9.8. A standard deviation of 2.51.

My problem is the following:

Use proper notation, write the “null” and “alternative” hypotheses for the population mean wage being less than $10. Use the data above to conduct this test using a level of significance (α) equal to 0.10. Show your work.

Any help would be greatly appreciated.

Thanks
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
You have to put forth a little more effort for us to help you. Try writing out the hypotheses and we will critique.


Sounds like a one-sample ttest or Wilcoxon sign test.
 
#3
You have to put forth a little more effort for us to help you. Try writing out the hypotheses and we will critique.


Sounds like a one-sample ttest or Wilcoxon sign test.

I've been trying to figure that out to begin with. It has been a while since I have done these. Are either of these correct?

H0: There is no statistically significant relationship between high school dropouts and their current wages.
H1: There is a statisically significant relationship between high school dropouts and their current wages thus leading to the hypothesis that the mean wage is less than $10.

H0: The population parameter is greater than or equal to $10
H1: The parameter is less than $10
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Ha: Population average wage < $10 at alpha = 0.10 level.
Ho: Population average wage >/= $10 at alpha = 0.10 level.


It has been over a decade since I have done these and the question does not explicitly say what the question is (< 10 is alternative or null, I am guessing the null).
 

Dason

Ambassador to the humans
#5
You don't typically mention the alpha in the hypothesis themselves. Silly nitpick but typically we write the null before the alternative. The statement you want to 'prove' is what you write as your alternative so I'd say you got the null and alternative correct after those changes.
 

Karabiner

TS Contributor
#6
H0: The population parameter is greater than or equal to $10
H1: The parameter is less than $10
H0 depends on the philosophy of your instructor.
Commonly, a research hypothesis such as: parameter < constant
does not requite a statistical hypothesis parameter >= constant .
Instead parameter = constant would be the Null.
But maybe they taught you otherwise, and you have to stick to it.

With kind regards

K.
 

ondansetron

TS Contributor
#7
I've been trying to figure that out to begin with. It has been a while since I have done these. Are either of these correct?

H0: There is no statistically significant relationship between high school dropouts and their current wages.
H1: There is a statisically significant relationship between high school dropouts and their current wages thus leading to the hypothesis that the mean wage is less than $10.
The bold should be removed from the hypotheses. Statistical significance is a property of a test that doesn't actually apply to the thing under study. In other words, a test can be "significant" at some alpha level, but a relationship either exists or it does not. The relationship is not "statistically significant," but the test can be.