Looking for assistance with the attached Statistics Homework practice. Need an answer key to work with.
1. You have been assigned to research effects of the dual credit programs on first term GPA’s in college. You have randomly selected a 30 students who did dual credit. And, you know the population information for first term college students. Given the below information, compute the Z-Test of the sample mean.
Parameters/ Statistics
Population Mean (µ) 2.5
Population Standard Deviation (σ) 0.8
Sample mean (X ) 2.7
Sample Size (n) 30
2. For the z-test in question 1, let’s assume your alternative hypothesis is directional (H1) μ>2.5 and your alpha (level of significance) was set at .05. What is your critical value? (Hint: one-tailed) Should you reject or retain the null hypothesis? Explain why?
3. For the z-test in question 1, let’s assume your alternative hypothesis is nondirectional (H1) μ=2.5 and your alpha (level of significance) was set at .05. What is your critical value? (Hint: two-tailed) Should you reject or retain the null hypothesis? Explain why?
4. For the z-test in question 1, let’s assume your alternative hypothesis is nondirectional (H1) μ=2.5 and your alpha (level of significance) was set at .01. What is your critical value? (Hint: Two-tailed) Should you reject or retain the null hypothesis? Explain why?
5. For the z-test in question 1, what is the probability of the sample mean as high or higher than 2.7?
6. If I decrease my alpha-level form 0.1 to .001, which decision error am I less likely to commit and which one am I more likely to commit? And how do you know this?
7. With data from Question 1, compute the 95% confidence internal and 99% Confidence internal for the sample mean.
8. If you only have the answer from Question 7, how would you know to reject or retain the null hypothesis at alpha .05? at alpha .01 ?
