(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.

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

Step-by-step explanation:

Information given

represent the sample mean

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:

  (1)

The degrees of freedom are given by:

The Confidence is 0.96 or 96%, the significance is and , and the critical value would be

Replacing the info we got:

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

b

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be