Question

Salt-free diets are often prescribed to people with high blood pressure. Eight volunteers participated in a study. Data was obtained from the experiment which was designed to estimate the reduction in diastolic blood pressure as a result of following a salt-free diet for two weeks. Assume diastolic readings are normally distributed.  The resulting mean difference is 1.25mmHg with a standard deviation of 2.4928mmHg.  Construct a 98% confidence interval for the mean reduction in the diastolic reading after two weeks on this diet.

Sample of data:

Before 93 106 87 .....

After 92 102 89....

ONLY the interval and interpretation are required;  you may omit Interpretation, Assumption, and Conditions.

As always, show work when calculations are necessary. Go out at least four decimal places if there are many significant digits.

Answer 1

Sol:

mean difference=Xd=1.25

difference in standard deviation=Sd=2.4928

n=8

df=n-1=8-=7

alpha=1-0.98=0.02

alpha/2=0,02/2=0.01

t crit in excel

=T.INV(0.01,7)

=2.997951567

98% confidenc einterval for mean difference ins

Xd-t*Sd/sqrt(n),Xd+t*Sd/sqrt(n)

1.25-2.997951567*2.4928 /sqrt(8),1.25+2.997951567*2.4928 /sqrt(8)

-1.392208,3.892208

98% confidence interval for mean difference

(-1.3922,3.8922)

we are 98% confident that the true  mean reduction in the diastolic reading after two weeks on this diet lies in between  -1.392208 and 3.892208