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# RES 342 Week 3 E-Text Assignments.

Homework

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Chapter 10
10.30 – In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility.
During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the
fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At a = .01, did the yellow fire
trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule
and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the
p-value and interpret it. (f) If statistically significant, do you think the difference is large enough
to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.
a)
H
0
: p
1
= p
2
H
a
: p
1
> p
2
b)
Reject H
0
if z > 2.326
c)
5
1 2
1 2
20 4
ˆ
8.322 10
153,348 135,035
X X
p x
n n
-
+ +
= = =
+ +
( )
( )
1 2
5 5
1 2
20 4
ˆ ˆ
153,348 135,035
2.961
1 1
1 1
8.322 10 1 8.322 10
ˆ ˆ
1
153,348 135,035
p p
z
x x
p p
n n
- -
-
-
= = =
æ ö æ ö
÷ ÷
ç ç
- +
÷ ÷
- +
ç ç
÷ ÷
÷
ç
ç
÷
ç
è ø
è ø
d)
Since the test statistic is in the rejection region, we reject the null hypothesis. We have sufficient
evidence to conclude that the yellow fire trucks significantly reduced the accident rate.
e)
p-value = 0.0015
Since the p-value is less than 0.01 we reject the null hypothesis.
f)
The difference is large enough at 1% level of significance. It's large for this sample.
g)
Normality might not be fulfilled because 4 is a very small (<5) number in the second group.

10.44
Does lovastatin reduce the risk of heart attacks? In a Texas study, researchers gave lovastatin to
2,325 people and inactive substitute to 2,081 people. After 5 years 57 of the lovastatin group had
sufford a heart attack, compared with the 97 for the inactive pill.
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p1 p2 p
c
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10.46
To test the hypothesis that students who finished an exam first get better grades. Professor
Hardtack kept the mean score of 77.1 with a standard deviation of 19.6 while the last 24 papers

handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant
difference at a=.05?
A) State the hypothesis for a right tailed test
B) Obtain a test statistic and p-value assuming equal variances.
C) Is the difference in the mean scores large enough to be important?
D) Is it reasonable to assume equal variances
E) Carry out a formal test for equal variances at a=.05, showing all steps clearly
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