A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 25 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day.
Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 12.7 pounds with a standard deviation of 2.2 pounds. The members of Group B had lost a mean of 10.8 pounds with a standard deviation 2.0 pounds during the same time period. Assume that the population variances are not the same.
Create and interpret a 95% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not.

(0.7044 ; 3.0956)

Step-by-step explanation:

Given:

GROUP A:

n1 = 25

x1 = 12.7

s1 = 2.2

GROUP B :

n2 = 25

x2 = 10.8

s2= 2.0

The obtain the confidence interval assuming unequal population variance :

(x1 - x2) ± tα/2[√(s1²/n1 + s2²/n2)]

The degree of freedom :

df = (s1²/n1 + s2²/n2)² ÷ (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1

The degree of freedom :

(2.2²/25 + 2²/25)² ÷ (2.2²/25)²/24 + (2²/25)²/24

df = 0.12503296 ÷ (0.0015617 + 0.0010666)

df = 47.57 ;

df = 48

Tcritical value ; α = 95% ; df = 48

Tcritical = 2.0106

C.I = (12.7 - 10.8) ± 2.0106[√(2.2²/25 + 2²/25)]

C.I = 1.9 ± (2.0106 * 0.5946427)

C.I = 1.9 ± 1.1955887

C. I = (0.7044 ; 3.0956)

i know the answer is 3

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.