In: Statistics and Probability
A friend of mine believes that the average GPA at KSU is equal to 3.0. In order to test whether he/she is right, I collect some information from the data. Specifically, I use 100 KSU students to form a sample and find that their sample average GPA is equal to 3.3. In addition, suppose that I also know the population standard deviation of GPA at KSU is 1.5. I decide to use 0.05 as the level of significance for my hypothesis testing. Could you help me with Q1-Q10 below?
Q1: What should be my null hypothesis? What should be my alternative hypothesis?
Q2: Is this a lower-tailed, upper-tailed or two-tailed case?
Q3: Show me how to calculate my test statistic.
Q4: If I use the critical value approach, explain how to derive my critical value(s).
Q5: If I use the p-value approach, explain how to derive my p-value.
Q6: If I use the confidence interval approach, show me how to derive the confidence interval.
Q7: How to make my decision, if I use the critical value approach?
Q8: How to make my decision, if I use the p-value approach?
Q9: How to make my decision, if I use the confidence interval approach?
Q10: Are the decisions in Q7, Q8, and Q9 the same?
(Q1)
H0: Null Hypothesis: = 3.0 ( the average GPA at KSU is equal to 3.0) (Claim)
HA: Alternative Hypothesis: 3.0 ( the average GPA at KSU is not equal to 3.0)
(Q2)
This is a two-tailed case
(Q3)
= 3.3
= 1.5
n = 100
Test Statistic is given by:
(Q4)
= 0.05
From Table, critical values of Z = 1.96
(Q5)
Z Score = 2.00
By Technology, p - value = 0.0455
(Q6)
Confidence Interval:
So,
Answer is:
(3.006, 3.594)
(Q7)
Since calculated value of Z = 2.00 is greater than critical value of z = 1.96, the difference is significant. Reject null hypothesis.
Conclusion:
The data do not support the claim that the average GPA at KSU is
equal to 3.0.
(Q8)
Since p - value = 0.0455 is less than = 0.05, the difference is significant. Reject null hypothesis.
Conclusion:
The data do not support the claim that the average GPA at KSU is
equal to 3.0.
(Q9)
Since 3.0 is not included in the confidence interval (3.006, 3.594), the difference is significant. Reject null hypothesis.
Conclusion:
The data do not support the claim that the average GPA at KSU is
equal to 3.0
(Q10)
The decisions in Q7, Q8, and Q9 are the same