Statistics: GPA Distribution, Significance Level, and Confidence Interval

Statistics
Name:
Institution:
21st February 2019

Question 1:
Past experience indicates that the distribution of GPAs in private college is normal with μ=2.5
and σ²=0.25 (compactly: x≃n (2.5, 0.25), where x = student’s GPA). Some people have claimed
however, that due to grade inflation the GPA has increased. Use a sample (random) of N=2.5 andx/= 2.68 to test the indicated claim at the 5% significance level. Would your answer be different
if you had tested at the 1% significance level? Which test would you prefer? Explain your
answer.
Answer
STEP 1:
We choose the significance level which in this case is α =0.05
The critical z value is 1.645. Reject H0 if Z > 1.645.
STEP 2:
We calculate the Z score
Z= ̄x−μ
σ /√ N = 2.68−2.5
0.25 / √2.5 = 0.18
0.1581 =1.1384
STEP 3:
From the computed Z score, we fail to reject the null hypothesis (H0) since Z < 1.645
STEP 4:
We conclude that there is no sufficient significant evidence to conclude that GPA has increased.
Yes the answer would be different if I had tested at the 1% significance level. I would prefer 1%
significance level instead of 5% significance level because 1% significance level is more
accurate than 5% significance level (Faherty, 2008).