1.
Dr. Andretti predicts that racecar drivers will have a greater tendency to make left hand instead
of right hand turns.
He recruits 32 race car drivers and has them drive down a narrow street,
which has just as many possible left hand turns as it has right hand turns.
He then records
whether the first turn that the drivers take is a left or right hand turn.
Help him test his
hypothesis by analyzing the data that he obtained with the appropriate statistical test:
Raw Data:
Turned Left
Turned Right
28
4
Solution.
..Run a chi square test to see if there is any preference.
Hypotheses:
Ho: Racecar drivers exhibit no preference.
H1: Racecar drivers exhibit a turning preference.
Calculation:
Turned Left
Turned Right
Observed:
28
4
Expected:
(16)
(16)
χ
2
=
Σ
(OE)
2
/E = (2816)
2
/16 + (416)
2
/16 = 18.00
df= (C1)= (21) = 1
Decision Rule:
χ
2
critical = 3.84
Result:
Reject Ho.
The racecar drivers had a preference for left hand turns.
2.
An anesthesiologist predicts that patients who use PainFree™ will report lower pain scores
following surgery than those using PainPax™.
Since she has had Psych 60, she knows to
randomly assign subjects to the drug conditions.
She is also concerned that the type of surgery
that the patient had might influence differences in selfreported pain scores between the two
groups.
Therefore, when assigning a patient to the second drug group, she or he is paired with
a patient in the first group who had the same type of surgery. Help her analyze her data by
stating the null and alternative hypotheses symbolically and running the appropriate statistical
test.
Use an alpha of .05.
Raw Data:
PainPax
PainFree
6
2
10
6
4
0
5
7
10
7
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5
6
3
9
4
Research Problem:
Do patients taking PainFree report lower pain scores than those taking PainPax, given that those
patients are originally matched for type of surgery?
Statistical Hypothesis:
Ho:
μ
mean difference
>
0
H1:
μ
mean difference
< 0
Where
mean difference
=
μ
PainFree

μ
PainPax
If PainFree has a lower mean than the Pain Pax group, then the mean difference under the
alternative hypothesis that you would be hoping for would be a mean difference value that is
negative, or less than zero.
Decision Rule:
Reject Ho at .05 level (directional test) if t <
1.89
Raw Data:
PainPax
PainFree
D
(Pain Free – Pain Pax)
D
2
6
2
4
16
10
6
4
16
4
0
4
16
5
7
2
4
10
7
3
9
9
5
4
16
6
3
3
9
9
4
5
25
25
111
Mean D =
3.125
Mean D
3.125
Standard error of mean D
0.766194
Standard deviation of D
2.167124
Calculations:
t = mean D / standard error of D =
3.125/.766 = 4.07
Decision:
Reject Ho.
Interpretation:
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 Winter '08
 Ard
 Statistics, Standard Deviation, Null hypothesis, mean difference

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