Medical researchers have developed a new artificial heart constructed primarily
ID: 3160487 • Letter: M
Question
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 four hours. A random sample of SO battery packs Is selected and subjected to a life test the average life of these batteries 15 4.05 hours. Assume that battery life is normally distributed with standard deviation sigma = 0.2 hour Test the claim that mean battery Me exceeds 4 hours using a 0.05 Type 1 error. State the hypothesis. Compute the test statistic. 1.77 2.77 0.77 3.77 Compute P-value. 0.01 0.06 0.08 0.04 Conclude the hypothesis test by justifying your answer.Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 4
Ha: u > 4 [ANSWER]
*******************************
b)
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 4.05
uo = hypothesized mean = 4
n = sample size = 50
s = standard deviation = 0.2
Thus, z = (X - uo) * sqrt(n) / s = 1.767766953 = 1.77 [ANSWER, A]
*******************************
c)
Also, the p value is, as this is right tailed,
p = 0.038549936 = 0.04 [ANSWER, D]
*********************************
d)
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the mean battery life eceeds 4 hours at 0.05 level. [CONCLUSION]