Question

In a randomized comparative experiment on the effect of dietary calcium on blood pressure, researchers divided 58 healthy white males at random into two groups. One group received calcium; the other, a placebo. At the beginning of the study, the researchers measured many variables on the subjects. The paper reporting the study gives x⎯⎯⎯=x¯=113.4 and s = 9.4 for the seated systolic blood pressure of the 29 members of the placebo group.

Give a 95% confidence interval for the mean blood pressure in the population from which the subjects were recruited is.

The confidence interval (±±0.1) is from ______ to _______

Answer 1

sample mean, xbar = 113.4
sample standard deviation, s = 9.4
sample size, n = 29
degrees of freedom, df = n - 1 = 28

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.048

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (113.4 - 2.048 * 9.4/sqrt(29) , 113.4 + 2.048 * 9.4/sqrt(29))
CI = (109.83 , 116.97)

109.83 to 116.97