Question

In an experimental treatment, a random individual scores 51 on a measurement. People in general are normally distributed with a mean of 37 and a standard deviation of 7. The researcher predicts that the treatment will create an effect on the subject, but does not specify if the measurement will increase or decrease. Using a 5% significance level (p < .05), what conclusions should this researcher make about the treatment. Utilize the five-step hypothesis testing process and show all of your work.

Answer 1

There is significant evidence that treatment will create effect on the subject. Hence We reject H0

Explanation:

H0 : μ = 37

H1 : μ ≠ 37

μ = 37 ; σ = 7 ; sample size, x = 51 ; sample size, n = 1

Decision region :

If P value < α ;

Reject H0

Using the Z test statistic :

Zstatistic = (x - μ) ÷ (σ / √n)

Zstatistic = (51 - 37) ÷ (7 / 1)

Zstatistic = 14 ÷ 7

Zstatistic = 2

Obtaining p value from Zstatistic using the p value calculator ;

Zscore = 2 ; 2-tailed test, significance level = 0.05

P value = 0.0455

Zcritical at α = 0.05 for a 2 - tailed test = 1.96

0.0455 < 0.05

There is significant evidence that treatment will create effect on the subject. Hence We reject H0