Question 294715: A doctor is using a method of treatment that is thought to be 94% successful. What is the probability that their are no failures in 15 treatments (round to the nearest hundredth)?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
-------
p-hat(red) = 20/153,348 = 1.304x10^-4
------------
yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135035 = 2.9622x10-5
-------------------
At α = .01, did the yellow fire trucks have a significantly lower accident rate?
One-tail z-test: Critical value = 2.326
(a) State the hypothesis.
Ho: p(red)-p(yellow) = 0
Ha: p(red)-p(yellow) < 0
-------------------------------
(b) State the decision rule and sketch it.
? Not sure what is meant by this.
-------------------------------
(c) Find the sample proportions and z test statistic.
Test statistic:
---
Note: p-bar= (4+20)/(153348+135035) = 8.3223x10^-5;q-bar=1-p-bar
-----------------------
Test statistic
z(1.0078x10^-4) = 1.0078x10^-4/sqrt[(p-bar)(q-bar)/n1 + (p-bar)(q-bar)/n2]
= 2.9610
(d) Make a decision.
Since the test statistic is greater than the critical value, reject Ho.
p(red) is not equal to p(yellow)
------------------------------------------
(e) Find the p-value and interpret it.
p-value = 0.0015 ; Only 0.15% of test results could have provided stronger
evidence for rejecting Ho.
-------------------------
(f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
I'll leave that to you
--------------------
(g) Is the normality assumption fulfilled? Explain.
Show that p(red)n1>5, q(red)n1>5
and p(yellow)n2>5, q(yellow)n2>5
=======================================
Cheers,
Stan H.
|
|
|
