AP Statistics Section 15 C
The most common hypothesis about the slope is
_________.
H 0 :   0 A regression line with slope 0 is
_________.
That is, the mean of y (does/does
horizontal
not) change when x changes. So this says that
there is no true linear relationship between x
and y. Put another way, says there is
___________
no correlatio n between x and y in the population
from which we drew our data. You can use the
test for zero slope to test the hypothesis of zero
correlation between any two quantitative
variables.
Note that testing correlation
makes sense only if the
observations are ______.
an SRS
The test statistic is just the standardized version of the leastsquares slope b.
To test the hypothesis compute the t statistic t 
b
SE b
Once again, we use the t-distribution with n - 2 degrees of
freedom and as always our p-value is the area under the
tail(s).
Regressions output from statistical software usually gives t
and its two-sided P-value. For a one-sided test, divide the Pvalue in the output by 2.
Example 15.6: The hypothesis H :   0 says that
crying has no straight-line relationship with IQ.
The scatterplot we constructed shows that there
is a relationship so it is not surprising that the
computer output given on the previous page of
notes give t = ______
3 . 07 with a two-sided P-value
of _____.
. 004 There is (strong/weak) evidence that
IQ is correlated with crying.
0
Example 15.7: A previous example (3.5) looked at how well
the number of beers a student drinks predicts his or her blood
alcohol content (BAC). Sixteen student volunteers at Ohio
State University drank a randomly assigned number of cans of
beer. Thirty minutes later, a police officer measured their BAC.
Here are the data.
Student:
1
2
3
4
5
6
7
8
Beers:
5
2
9
8
3
7
3
5
0.10
0.03
0.19
0.12
0.04
0.095
0.07
0.06
Student:
9
10
11
12
13
14
15
16
Beers:
3
5
4
6
5
7
1
4
0.02
0.05
0.07
0.10
0.085
0.09
0.04
0.05
BAC:
BAC:
Here is the Minitab output for the blood alcohol content data:
The regression equation is
BAC = - 0.0127 + 0.0180 Beers
Predictor
Coef
StDev
T
P
Constant
-0.01270
0.01264
-1.00
0.332
Beers
0.017964
0.002402
7.48
0.000
S = 0.02044
R-Sq = 80.0%
Note: the actual calculated values are slightly different from these
Test the hypothesis that the number of beers has no effect on
BAC.
Hypotheses: The population of interest is
__________________
college students OSU
H0: _______
  0 In words,
____________________________
the # of beers has no effect on BAC
H1: _______
  0 In words,
_________________________________
the # of beers has a positive effect on BAC
where  is
___________________________
the slope of the true regression line
Conditions:
Seems safe to assume we have an SRS and responses are independen t.
Scatterplo t and residual plot indicate a linear relationsh ip
Residual plot shows constant standard deviation of the responses about LSL
Analysis
shows approximat ly Normal distributi on to for the residuals
Calculations:
P - value  .000
7.48
t  7 . 48
NOTE :
t
b
SE b

. 017964
. 002402
 7 . 48
Interpretation:
At any common significan ce level we reject H 0 and conclude that an
increase in the number of beers will cause an increase in BAC.