Question

Question 31 2 pts

A sample of n = 16 individuals is selected from a population with µ = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33.

If the sample variance is s2 = 16, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r2 to measure the size of the treatment effect.

Use a two-tailed test with α = .05.

Answer 1

We have given : A sample of n = 16

a population with µ = 30.

sample mean is found to be M = 33.

the sample variance is s2 = 16, therefore s = 4

then conduct a hypothesis test to evaluate the significance of

the treatment effect = (M - µ) / s  

= ( 33 - 30) / 4 = 0.75 , it is high

and calculate r2 to measure the size of the treatment effect. = it is not valid for this we need two samples .

Use a two-tailed test with α = .05.

## To test : Ho : µ = 30 vs H1 : µ ≠ 30

## test statistics : t = ( M - µ) * √ (n) / s

t = ( 33 - 30 ) * 4 / 4

t = 3

## t_crit = here degree of freedom is (n-1 ) = 15

used t critical value table : 2.1314 (from table)

## Decision : we reject Ho if t statistics value is greater than t critical value .

here t statistics value is greater than t critical value hence here we reject Ho .

## Conclusion : there is enough evidence to conclude that population mean is differ than 30 ie ( µ ≠ 30)