question archive A UCLA researcher claims that the average life span of mice can be extended by as much as 8 months when the calories in their diet are reduced by approximately 40% from the time they are weaned
A UCLA researcher claims that the average life span of mice can be extended by as much as 8 months when the calories in their diet are reduced by approximately 40% from the time they are weaned
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A UCLA researcher claims that the average life span of mice can be extended by as much as 8 months when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diets are enriched to normal levels by vitamins and proteins. Suppose that a random sample of size 10 mice is fed a normal diet and has an average life span of 32.1 months, with a standard deviation of 3.2 months, while a random sample of 15 mice is fed the restricted diet and has average life span of 37.6 months with a standard deviation of 2.8 months. Test the hypothesis at the 0.05 level of significance, that the average life span of mice on this restricted diet is increased by 8 months against the alternative that the increase is less than 8 months. Assume the distribution of life spans for the regular and restricted diets are approximately normal.
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Answer:
sample size,n
sample mean,x
standard deviation,s
alpha,a = 0.05
n1= 10 , x1= 32.1 , s1= 3.2000
n2= 15 , x2= 37.6 , s2= 2.8000
H0: u1 = u2
H1: u1 < u2
standard error, SE = sqrt((s1^2/n1)+(s2^2/n2)
SE = 1.24365
test statistic, t = (x1-x2) / SE
t = -4.422
critical value = -t(a,n1+n2-2) = -t(0.05,23)
critical value = -1.714
since t < critical value, hence reject H0
so we conclude that the average life span of mice on this restricted diet is increased by 8 months against the alternative that the increase is less than 8 months
