Question

(23.01) 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⎯⎯⎯=113.7 and s = 9.1 for the seated systolic blood pressure of the 29 members of the placebo group. Give a 96% confidence interval for the mean blood pressure in the population from which the subjects were recruited is.

Answer 1

`113.7-2.154(9.1)/(√(29))=110.06`

`113.7+2.154(9.1)/(√(29))=117.34`

And the 96% confidence is given by (110.06; 117.34)

Explanation:

Information given

`\bar X=113.7` represent the sample mean

`\mu` population mean (variable of interest)

s=9.1 represent the sample standard deviation

n=29 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

The degrees of freedom are given by:

`df=n-1=29-1=28`

The Confidence is 0.96 or 96%, the significance is
`\alpha=0.04` and
`\alpha/2 =0.02`, and the critical value would be
`t_(\alpha/2)=2.154`

Replacing the info we got:

`113.7-2.154(9.1)/(√(29))=110.06`

`113.7+2.154(9.1)/(√(29))=117.34`

And the 96% confidence is given by (110.06; 117.34)