7
Chapters 9-10-11 – Summary Notes
Chapter 9 – Inferences from Two Samples (Be sure to use Hypothesis Test Checklist)
Means (9-3) (independent samples)
Matched Pairs (9-4) (dependent samples)
Hypothesis Test
(Be sure to use Hypoth
Test checklist)
Calculator: 2-PropZTest
Formulas:
H
0
: p
1
= p
2
; H
1
: p
1
< or > or ≠ p
2
Calculator: 2-SampleTTest
H
0
: µ
1
= µ
2
; H
1
: µ
1
< or > or ≠ µ
2
Calculator: (1) Enter data in L1 and L2, L3
equals L1 – L2; (2) TTest (which gives you all the
values you need to plug into the formula)
H
0
: µ
d
= 0; H
1
: µ
d
< or > or ≠ 0
No formulas. If interval contains 0, then fail to reject. If for a 1-tail Hypo. Test is .05, the CL for Conf. Int. is 0.9 (1 - 2).
Chapter 10 – Correlation and Regression (don’t use formulas, just calculator; the important thing is interpreting results.)
Calculator and Interpretation (Anderson: show value of t but not formula)
Hypothesis Test: Is there a linear
correlation between two variables,
x and y? (10-2)
r is the sample correlation
coefficient. It can be between -1
and 1.
Calculator: Enter data in L1 and L2, then STAT > Test > LinRegTTest. (Reg EQ > VARS, Y-VARS, Function, Y1). P-Value tells
you if there is a linear correlation. The test statistic is r, which measures the strength of the linear correlation.
Interpretation: x is the explanatory variable; y is the response variable. H
0
: there no linear correlation; H
1
: there is a linear
correlation. So, if P-Value < , you reject H
0,
so there IS a linear correlation; if P-Value > , you fail to reject H
0,
so there is
NO linear correlation.
Calculator: To create a scatterplot: Enter data in L1 and L2, then LinRegTTest; then 2
nd
Y = Plot 1 On, select correct type
of plot. Then Zoom 9 (ZoomStat). To delete regression line from graph, Y= , then clear equation from Y1.
When you have 2 variables x and y,
how do you predict y when you are
given a particular x-value? (10-3)
Two possible answers:
(1) If there is a significant linear correlation, then you need to determine the Regression Equation (y = a + bx; LinRegTTest
gives you a and b), then just plug in the given x-value. Or the easy way to find y for any particular value of x:
Calculator: VARS Y-Vars 1:Function Enter Enter Input x-value in parentheses after Y1
(2) If there is no significant linear correlation, then the best predicted value for y = . Calculator: VARS, 5, 5, ENTER.
When you have 2 variables x and y,
how do you predict an interval
estimate for y when you are given
a particular x-value? (10-4)
1. PROGRAM, INVT ENTER Area from left is 1-/2, DF = n-2. This gives you t Critical Value.
2. PROGRAM, PREDINT ENTER Input t Critical Value from Step 1, then input X value given in the problem. Hit Enter twice
to get the Interval.
How much of the variation in y is
explained by the variation in x?
(10-4)
The percentage of variation in y that is explained by variation in x is r
2
, the coefficient of determination.
Calculator: to find r
2
, enter data in L1 and L2, then LinRegTTest. It will give you r
2
. 1 sentence conclusion: “[r
2
]% of the
variation in [y-variable in words] can be explained by the variation in [x-variable in words].”
Total Variation is
. Explained Variation is Total Variation times r
2
. Unexplained Variation is Total Variation
minus Explained Variation. To find them all, put x values in L1; put y values in L2; LinRegTTest; then PRGM VARATION.