Vascular. A study of nine preteen females finds that extended periods of uninter

Question

Vascular. A study of nine preteen females finds that extended periods of uninterrupted sitting are associated with reduction in vascular function. The sampled reduction amounts are indexed values provided below. Assume normality for the population of reduction values. 2.22 1.61 2.12 1.65 1.53 1.18 2.58 1.19 1.37 Compute the sample mean and standard deviation. Hint = 15.45 and 2x2-2842. Compute the 95% confidence interval for the true mean vascular function reduction amount under these conditions. Does the interval suggest 2.0 is a plausible value for the true mean reduction amount? Does the interval suggest 2.2 is a plausible value for the true mean reduction amount? a) b) c) d)

Explanation / Answer

a)

mean = sum(Xi)/n = 1.71667

var = sum(Xi-Xbar)^2/(n-1) 0.2372

sd=sqrt(var)= 0.487031826

b)

95% CI = Mean +- t(a/2,n-1)*(sd/sqrt(n))

t(a/2,n-1) 2.306004135

lower =1.71667-2.306004*( 0.487032/SQRT(9)) = 1.342304087

upper =1.71667+2.306004*(0.487032/SQRT(9)) = 2.091035913

C)since the confidence interval contains the value 2, I can say that, 2 is a possible value for the true mean deduction amount

D) since the confidence interval doesn't contain the value 2.2, I can't say that, 2.2 is a possible value for the true mean deduction amount

XI (xi-xbar)^2 2.22 0.253344 1.61 0.011378 2.12 0.162678 1.65 0.004444 1.53 0.034844 1.18 0.288011 2.58 0.745344 1.19 0.277378 1.37 0.120178 sum 15.45 1.8976 sum/n 1.716666667 sum/(n-1) 0.2372

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