Question

data from four identical trials on a new sleep herb are shown in the table. complete parts (a) and (b)

group	number of subjects	number who reported better sleep
b	170	35
c	210	48
d	190	40

b. the next trial will have 1,000 subjects. what is a reasonable prediction for the next trial?
in the next trial, the herb should be effective in improving sleep for about people.
(round to the nearest integer as needed.)

Explanation:

Step1: Calculate total number of subjects

$250 + 170+210 + 190=820$

Step2: Calculate total number of people who reported better sleep

$55 + 36+48 + 40 = 179$

Step3: Calculate the proportion of people who reported better sleep

$\text{Proportion}=\frac{179}{820}\approx0.2183$

Step4: Answer for part (a)

The proportion represents the average number of people for whom the herb is effective in any group. So in any group of people, the herb is effective in improving sleep for about $0.2183$ of the group.

Step5: Answer for part (b)

For a trial with 1000 subjects, the predicted number of people for whom the herb is effective is $1000\times0.2183 = 218.3\approx218$

Answer:

a. $0.2183$ of the group
b. $218$