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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 13

Lesson 2: Testing for the slope of a regression model

# Using a P-value to make conclusions in a test about slope

AP.STATS:
DAT‑3 (EU)
,
DAT‑3.M (LO)
,
DAT‑3.M.1 (EK)
,
DAT‑3.N (LO)
,
DAT‑3.N.1 (EK)
,
DAT‑3.N.2 (EK)
Making conclusions in a hypothesis test about the slope of a least-squares regression line.

## Want to join the conversation?

• I wonder what degrees of freedom is taken in this sample? If we assume that it is a large sample, we can use a z-statistic. In this case p-value will be 0.00136. • in fact we can at least try to infer DF(degree of freedom) using t_table

unfortunately i have a t_table only with columns for 0.01 and 0.002 as two-tail probability. but we have to make an inference for 0.004 which is given. thus we find a closest value of t(=2.999) between these two columns

and that t_value is 3.098 with DF of 1000 for 0.002 tail prob. and for 0.01 tail prob, t_value is 2.581 with same DF

now let's make a leap of faith that t_value shrinks quite linearly with tail prob. meaning if we move from 0.002 tail prob to 0.01 tail prob, the value of 3.098 may decrease to 2.581 in a bit expected manner. regarding the shape of this edge of t_distribution, this might not that large leap i believe

then 0.004 must be 1/4 left to the 0.002 tail prob, thus we can assume 3.098 - (3.098-2.581)/4 = 3.098 - 0.517/4 = 3.098 - 0.129 = 2.969. this is not that distant from our expected 2.999 of tail prob

thus i would bet that DF used in this example might be slightly less than 1000 (but not close to 100)
• Hi Sal,
You mention at that the p-value is related to the alternative hypothesis. I thought the p-value is p(β> estimated β | B0 is True). So in a way it is not related to the alternative hypothesis. Could you please explain?
Best,
Alaa
(1 vote) • Isn't the "constant" the independent variable? Therefore price should be on the x axis and speed on the y?
(1 vote) • What if the slope turns out to be negative? Neither of the hypotheses include a negative outcome, so what would you conclude if that was the case?
(1 vote) 