Mrs. Grant wishes to compare the performance of sixth-grade students in her district with the national norm of 100 on a widely used aptitude test. The results for a random sample of her sixth graders...

Mrs. Grant wishes to compare the performance of sixth-grade students in her district with the national norm of 100 on a widely used aptitude test. The results for a random sample of her sixth graders lead her to retain Ho:µ = 100 (x - .01) for her population. She concludes, “My research proves that the average sixth grader in our district falls right on the national norm of 100”. What is your reaction to such a claim?
9. State the critical values for testing Ho:µ -=500 against H1:µa. x = .01
b. x = 0.5
c. x = .10
20. Suppose a researcher wishes to test
Ho:µ = 100 against
H1:µ >100 using the .05 level of significance; however, if she obtains a sample mean far enough below 100 to suggest that
Ho is unreasonable, she will switch her alternative hypothesis to
H1: ? 100 (æ = .05) with the same sample data. Assume
Ho to be true. What is the probability that this decision strategy will result in a Type I error? (Hint: sketch the sampling distribution and put in the regions of rejection).
4. Repeat problem 2a and 2b with
n
= 9 and then
n
= 100. What generalization is illustrated by a comparison of the two sets of answers (i.e.,
n
= 9 versus
n
= 100).
(Problem 2a : x =33.10 (n = 36) – calculate Qx.)
(Problem 2b : Construct the 95% confidence interval for her population mean score.
5. Consider problem 4 in chapter 11 where X = 48, n = 36, and Q = 10.
a. Construct a 95% confidence interval for µ.
b. Construct a 99% confidence interval for µ.
10. For a random sample, X = 83 and n = 625; assume ø = 15.
a. Test
H0: µ = 80 against
H1: ? 80 (œ = .05). What does this tell you about µ?
b. Construct the 95% confidence interval for µ. What does this tell you about µ?
c. Which approach gives you the more information about µ? (Explain).
9. From Table B, identify the value
t
for that df = 15.
a. is so high that only 1% of the
t
values would be higher
b. is so low that only 10% of the
t
values would be lower.
13. The task in particular concept-formation experiment is to discover, through trial and error, the correct sequence in which to press a row of buttons. It is determined from the nature of the task that the average score obtained by random guessing alone would be 10 correct out of a standard series of trials. The following are the scores for a sample of volunteer college students: 31, 24, 21, 25, 32. You wish to determine whether such subjects do better, on the average, than expected by just guessing.
a. Set up
H0 and
H1.
b. Determine
t. 05.
c. Perform the statistical test
d. Draw final conclusions.