"In a research report, Richard H. Weindruch of the UCLA Medical School claims that mice with an average life span of 32 live to be about 40 months old when 40% the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ> 40 if n = 60 mice that are placed on this diet have an average life of x= 35 months with a standard deviation s=5.8 months? a= 0.05
Answers
Answer:
Many comments, some confusion, maybe no resolution:
Seems to me this is a left-sided, 1-sample t test of H0:μ=40 against H1:μ<40 based on sample mean and standard deviation X¯=38,S=5.8, respectively, for n=64 random observations from a normal sample. Output from a recent release of Minitab, which accepts summarized data:
One-Sample T
Test of μ = 40 vs < 40
N Mean StDev SE Mean 95% Upper Bound T P
64 38.000 5.800 0.725 39.210 -2.76 0.004
I will leave it to you to show how to obtain the T statistic (following @Henry's Comments) and to show that you reject H0 at the 5% level (or even the 1% level).
It is easy to see that X¯=38<40. You have evidence that it is significantly less than 40, in a statistical sense.
Note: DF=64−1=63 for the T-statistic. P-value from R statistical software, where pt is the CDF of a t-distribution:
pt(-2.76, 63)
[1] 0.003780076