Question

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?

Answer 1

The solution of the questions is given as

a)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments. (This is a two-tailed case)

c)

Test Statistic is given by:

z= 2.00

d)

Critical values of Z come from the table and equal $\pm$1.96.

e)

, p-value = 0.0455

f)

CI= (3.006, 3.594)

g)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

What is the null hypothesis?

a)

The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments.

c)

Test Statistic is given by:

$z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100$

z= 2.00

d)

$\alpha = 0.05$

Critical values of Z come from the table and equal $\pm$1.96.

e)

Z Score = 2.00

reading from table, p-value = 0.0455

f)

Confidence Interval:

$CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}$

$CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}$

CI= (3.006, 3.594)

g)

The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i)

The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.

Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

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