Medical researchers have developed a new artificial heart constructed primarily
ID: 3225422 • 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 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 sigma = 0.2 hour. Use alpha = 0.05. (a) Is there evidence to support the claim that mean battery life exceeds 4 hours? (b) Compute the power of this test if the true mean battery life is 4.5 hours. (e.g. 98.76). (c) What sample size would be required if we want to detect a true mean battery life of 4.5 hours if we wanted the power of the test to be at least 0.90?Explanation / Answer
Part-a
From following results we suppor the claim that mean>4 as p-value=0.039<0.05
One-Sample Z
Test of mu = 4 vs > 4
The assumed standard deviation = 0.2
95% Lower
N Mean SE Mean Bound Z P
50 4.0500 0.0283 4.0035 1.77 0.039
PArt-b
Power=1.00
Power and Sample Size
1-Sample Z Test
Testing mean = null (versus > null)
Calculating power for mean = null + difference
Alpha = 0.05 Assumed standard deviation = 0.2
Sample
Difference Size Power
0.45 50 1
Part-c
Sampel size=2
Power and Sample Size
1-Sample Z Test
Testing mean = null (versus > null)
Calculating power for mean = null + difference
Alpha = 0.05 Assumed standard deviation = 0.2
Sample Target
Difference Size Power Actual Power
0.45 2 0.9 0.937869