8. 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:µ<500, where
a. 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.
