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RES 342 Week 3 E-Text Assignments.

RES 342 Week 3 E-Text Assignments.

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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.

: p

= p

: p

> p

Reject H

if z > 2.326

1 2

20 4

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

8.322 10 1 8.322 10

ˆ ˆ

153,348 135,035

p p

x x

p p

n n

- -

= = =

æ ö æ ö

÷ ÷

ç ç

- +

÷ ÷

- +

ç ç

÷ ÷

è ø

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.

p-value = 0.0015

Since the p-value is less than 0.01 we reject the null hypothesis.

The difference is large enough at 1% level of significance. It's large for this sample.

Normality might not be fulfilled because 4 is a very small (<5) number in the second group.

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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

-/0 /11 20 * 

034-2-

534-6



0/4//

1 *)

03 53 02555 7

-2-0 -6 //1 

-- #

 8#

00 

255 8

220%0 *9'

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;)9<=)$>

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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

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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) H0: p1?= p2 Ha: p1?> p2 b) Reject H0 if z > 2.326 c) 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 ( ...
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