medical researchers have developed 1. Medical researchers have developed a new a
ID: 3333115 • Letter: M
Question
medical researchers have developed 1. Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart wil 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
Given that,
population mean(u)=4
standard deviation, =0.2
sample mean, x =4.05
number (n)=50
null, Ho: =4
alternate, H1: >4
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 4.05-4/(0.2/sqrt(50)
zo = 1.76777
| zo | = 1.76777
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.76777 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 1.76777 ) = 0.03855
hence value of p0.05 > 0.03855, 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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