hypothesis statement and conclusion

jordan

reference final exam review question #7 part (a) and (d):

is the null Ho: Slope is 0
Ha: Slope is not 0

I feel like we would reject the null because of two reasons:
I. Because the slope is not 0 in the table (its 5.7984)
II. The line is literally slanted on the graph itself

Is my reasoning sound and deductively/inductively acceptable?

mark

@jordan said:
reference final exam review question #7 part (a) and (d):
I feel like we would reject the null because of two reasons:
I. Because the slope is not 0 in the table (its 5.7984)
II. The line is literally slanted on the graph itself

I agree that you would reject the null neither of your reasons are relevant.

Remember that the slope computation of 5.7984 arises from a sample. If you collect another sample, you'll get a different slope. Neither of those are the actual slope but, presumably, they are close to the slope. The question is - "how confident are you that the slope is not zero"? This depends not only on the computed value but also the standard error. Ultimately, we express our level of confidence using the $p$-value. That's how hypothesis testing works!!