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 α= .01, did the yellow fire trucks have a significantly lower accident rate?
a) State the hypothesis
Ha: p(red)-p(yellow) is not greater than 0
b) State the decision rule and sketch it.
One-tail test with alpha=1%: critical value is z = 2.326
c) Find the sample proportions and z test statistic.
d) p-hat(red)= 20/153,348 ; p-hat(yellow) = 4/135,035
For Pooling: p-barbar = (20+4)/(153348+135035) = 0.00002.08..
z = [(20/153,348)-(4/135,035)]/sqrt[(0.00002.08)(0.999979)/153348 + (0.00002.08)*0.999979/135035)] = 2.960988...
e) Make a decision
Since the test statistic is greater than the critical value, Reject Ho
f) Find the p-value and interpret it.
p-value = P(2.960988 < z < 10) = 0.00153...
There is 0.1533% chance that the test would produce stronger evidence
g) If statistically significant, do you think the difference is large enough to be important? If so, to whom and why?
Yes it is statistically significant; the yellow paint has helped reduce
h) Is the normality assumption filled? Explain
Yes: p1n1 > 5 , q1n1>5 ;p2n2 > 5 , p2n2 > 5
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill.
a) State the appropriate hypotheses.
Ho: p(inactive) - P(active) =0
Ha: p(inactive) - p(active) > 0
p-hat(inactive) = 97/2081 = 0.0466... [continues]
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