Of all of the individuals who develop a certain rash, suppose the mean recovery time for individuals who do not use any form of treatment is 30 days with standard deviation equal to 8. A pharmaceutical company manufacturing a certain cream wishes to determine whether the cream shortens, extends, or has no effect on the recovery time. The company chooses a random sample of 100 individuals who have used the cream, and determines that the mean recovery time for these individuals was 28.5 days. Does the cream have any effect

z(s) is in the rejection  region. We reject  H₀. We dont have enought evidence to support that the cream has effect over the recovery time

Step-by-step explanation:

Sample information:

Size     n = 100

mean   x = 28,5

Population information

μ₀  =  30

Standard deviation  σ   = 8

Test Hypothesis

Null Hypothesis          H₀                x =  μ₀

Alternative Hypothesis   Hₐ           x <  μ₀

We assume CI = 95 %   then α = 5 %    α = 0,05

As the alternative hypothesis suggest we should develop a one tail-test on the left ( we need to find out if the cream have any effect on the rash), effects on the rash could be measured as days of recovery

A z(c) for 0,05 from z-table is:  z(c) = - 1,64

z(s) = ( x - μ₀ ) / σ/√n

z(s) = ( 28,5 - 30 ) / 8/√100

z(s) = - 1,5 * 10 / 8

z(s) =  - 1,875

Comparing z(s)  and z(c)

|z(s)| < |z(c)|        1,875  > 1,64

z(s) is in the rejection  region. We reject  H₀. We dont have enought evidence to support that the cream has effect over the recovery time

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: