(SHOW ALL WORK) Lifespan: Assume the average life-span of those born in the U.S.
ID: 3128063 • Letter: #
Question
(SHOW ALL WORK) Lifespan: Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at Live-Longer-USA (fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 40 people on this program have died and the mean age at death was 83.3 years.
(a) Calculate the probability that a random sample of 40 from the general population would produce a mean age-of-death greater than 83.3 years.
(b) Does this provide good evidence the the acorns and exercise program helps people live longer?
(c) Why could we use the central limit theorem here despite the parent population being skewed?
Explanation / Answer
(SHOW ALL WORK) Lifespan: Assume the average life-span of those born in the U.S. is 78.2 years with a standard deviation of 16 years. The distribution is not normal (it is skewed left). The good people at Live-Longer-USA (fictitious) claim that their regiment of acorns and exercise results in longer life. So far, 40 people on this program have died and the mean age at death was 83.3 years.
(a) Calculate the probability that a random sample of 40 from the general population would produce a mean age-of-death greater than 83.3 years.
Standard error = sd/sqrt(n) =16/sqrt(40) =2.5298
Z value for 83.3, z =(83.3-78.2)/2.5298 =2.02
P( mean x >83.3) =P( z > 2.02) =0.0217
(b) Does this provide good evidence the acorns and exercise program helps people live longer?
Since the calculated=0.0217 which is < 0.05, the data does provide good evidence the acorns and exercise program helps people live longer.
(c) Why could we use the central limit theorem here despite the parent population being skewed?
Since sample size 40 which is large ( >30), the sample mean is distributed as approximately normal, whatever the parent population.
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