Wanted to see if my solution is correct...

2) In an experimental treatment, a random individual scores 51 on a measurement. People for this treatment are normally distributed with a population mean of 37 and a population 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 the outcome. Using a 5% significance level ( = 0.05), what conclusions should this researcher make about the treatment? Utilize the five-step hypothesis testing process and show all your work. Data is unitless.

Soln

i. Null hypothesis; H₀: the treatment will not affect the subject

ii. Alternative hypothesis; H₁: the treatment will have either a positive or negative effect on the subject

iii. Significance level () = 0.05

iv. Test Statistic and Corresponding P-Value:

Mean() =37

Standard deviation () =7

X =51

Z score=

Considering a normal distribution;

P= (x>51)

=P (Z>)

=P (Z>)

= P (Z>2)

From statcrunch,

P(x>2) = 0.02275

= 2.27%

The probability that the score will increase or be more than 51 is 2.27%. Therefore, the probability that the measure will decline after the treatment is 97.73%. Also, since the P-value is a lesser amount than 0.05, we reject the null hypothesis. Thus, the treatment will decrease the outcome.