1. Medical researchers have developed a new artificial heart constructed primari

Question

1. Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needs to be recharged about every 4 hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume that battery life is normally distributed with standard deviation of 0.2 hour. a) Is there evidence to support the claim that mean battery life exceeds 4 hours? Use =0.05. b) What is the P-Value for the test in part a)? Make conclusions using this approach.

Explanation / Answer

Test Used: Z-Test For Single Mean
Set Up Hypothesis
Null Hypothesis H0: U=4
Alternate Hypothesis H1: U>4
Test Statistic
Population Mean(U)=4
Given That X(Mean)=4.05
Standard Deviation(S.D)=0.2
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=4.05-4/(0.2/Sqrt(50)
Zo =1.7678
| Zo | =1.7678
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.7678 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 1.7678 ) = 0.0385
Hence Value of P0.05 > 0.0385, Here we Reject Ho

ANSWERS
---------------
null, Ho: =4
alternate, H1: >4
test statistic: 1.76777
critical value: 1.645
decision: reject Ho
p-value: 0.03855
mean battery life exceeds 4 hours

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