The following data on maximum weight of lift (MAWL, in kg) for a frequency of four lifts/min was
reported in the paper “The Effects of speed, Frequency, and Load on Measured Hand Forces for a
Floor-to-Knuckle Lifting Task.” Subjects were randomly selected from the population of healthy
males aged 18-30. Assuming that MAWL is normally distributed, does the data suggest that the
population mean MAWL exceeds 25? Carry out a test using a significance level of 0.05
25.8 36.6 26.3 21.8 27.2
In the solution the teacher said H_0: m= 25; H_1: m>25
Why did she put the test in this manner? I instead did H_0: m>25 ; H_1: m<or= 25. How can I understand the way I shall lay down the test, like what is H_0 and H_1? Thank you very much.
The claim appears to be
So, I would write(as you did):
Upon running the test, we find
This results in a p-value of 0.1789, critical value of 2.1318, test stat of 1.0382
By looking at the p value, it is certainly > 0.05. Therefore, we do not reject the null hypothesis. There is not enough evidence at the 0.05 level to supoort the claim that the mean is > 25.
I do not know why your teacher wrote = instead of less than or equal to.
I suppose they had their reasons. Doing that, we still would not have nough evidence to support the claim. Maybe I am not up on things enough, but I have not seen the respective hypotheses written that way: With an equals for the null and a 'greater than' for the alternate hypothesis. I think we should keep it simple as possible.
I thought that maybe she did like that because she means that:
when we want data to provide enough evidence we put the claim in the alternative hp, because if we put it in the null hp we do not get the strong evidence, but just an impossibiity to refuse
when they ask if we can reject something, like that women are usually underpaid, we put it in H null, because we want to find that we reject it, and if we put it in H_0 and reject it is a strong rejection
Do you think it is a feasible reasoning?(I really tried to express what I mean as clear as possible)