Application Problems--General
1. Test the hypothesis: Ho: mu = 10
Ha: mu NE 10
given: alpha = .05
Mean = 6
Sigma = 5
n = 25
2. Given Mean = 67, Sigma = 3, n = 100, test the hypothesis that mu = 66,
alternative that mu ne 66, with alpha = .01.
Indicate all of the following:
A. test hypothesis
B. alternative hypothesis
C. test statistic Ha:
D. critical region
E. your conclusion
3. Given Mean = 67, s = 3, n = 100, test the hypothesis that mu = 66, alternative
mu ne 66, with alpha = .01.
Indicate all of the following:
A. test hypothesis
B. critical region
C. your conclusion
D. How does the critical region compare with that of prob. 2?
4. In each of the following cases, indicate whether a Type I error, a Type
II error, or no error was commited by the researcher:
Researcher decision
Ho Ha True value of mu based on Mean
A. mu = 0 mu ne 0 0 Reject Ho
mu = 0 mu ne 0 40 Reject Ho
mu = 0 mu ne 0 0 Do not reject Ho
mu = 0 mu ne 0 60 Do not reject Ho
5. In each of the following instances indicate whether the critical region
for rejection of H lies in the upper (right) tail, lower (left) tail, or
is divided between both tails of the sampling distribution of means for
mu = 0:
A. Ho: mu = 0, Ha: mu ne 0
B. Ho: mu = 0, Ha: mu gt 0
C. Ho: mu = 0, Ha: mu lt 0
6. Researcher Rowe is testing Ho: mu = 0 at the alpha = .05 level with
a sample size of 25, and he sets his critical values of Mean appropriately.
Researcher Null is testing Ho: mu = 0 at the alpha = .05 level with a sample
size of 100, and he sets his critical values of Mean appropriately.
- A. Does Rowe or Null have the larger probability of committing
a Type I error, or is the probability the same for both? Explain your answer.
- B. If mu is actually 10, does Rowe or Null have the larger
probability, Beta, of committing a Type II error? Explain your answer.
- C. Which researcher is performing a significance test that
has greater power to reject Ho if mu = 20? Explain your answer.
Return to Statistical Methods Index Page