Fall, 2013STA 2122, Social Science StatisticsD. Saha
Name: ______
Test 3
Chapters 9 - 11
Directions: For multiple choice questions circle your selection.
For short answer questions write your answer neatly in the space provided.
For computation questions space is provided for you to work out the answer. Please
identify your answer clearly.
For SPSS problems, another page will be provided.
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1. The t distribution is used when the population mean is not known.
T. trueF. false
2. When using the t distribution, the sample standard deviation is used as a point estimate of
the population standard deviation.
T. trueF. false
3. Why is the t statistic more variable than the z statistic?
A. The extra variability is from using degrees of freedom.
B. The extra variability is from using the sample mean.
C. The extra variability is from using the sample variance.
D. None of the above.
4. For a sample with n = 4, SS = 60, what is the sample variance? ______
5. For a sample with n = 4, SS = 48, what is the value of the standard error of the mean?
A. 1B. 2C. 4D. 8
6. For a sample with mean M = 135 and variance s2 = 45, the standard error of the mean is 3.
How large is the sample?
A. 2B. 3C. 5D. 9
7. As the sample size increases, the standard error of the mean ______.
A. increasesB. decreases
C. stays the sameD. cannot be determined
8. If all other factors were to remain unchanged, which of these conditions would produce a
a significant t?
A. n = 25, s2 = 100B. n = 25, s2 = 400
C. n = 100, s2 = 100D. n = 100, s2 = 400
9. If all other factors were to remain unchanged, which of these conditions would most likely
reject a null hypothesis that μ = 80?
A. n = 25, M = 85B. n = 25, M = 90
C. n = 100, M = 85D. n = 100, M = 90
10. Given α = .01 and n = 16, what is the critical value for a two-tailed t test?
A. .2.583B. 2.583C. 2.921D. 2.947
11. A sample has mean M = 39.5, standard deviation s = 4.3, and produces a t statistic of 2.14.
For a two-tail test, which of these statements is true.
A. You would reject H0 with α = .05, but not with α = .01.
B. You would reject H0 with α = .05, or with α = .01.
C. You would not reject H0 with α = .05, or with α = .01.
D. More information is needed to make a decision about H0.
12. A sample produces a t statistic of 2.20. For a two-tail test with α = .05, how large does the
minimum sample size to reject the null hypothesis?
A. n = 11B. n = 12C. n = 13D. n = 14
13. How does sample variance influence …
(a) … the likelihood of rejecting the null hypothesis?
(b) … the measure of effect size, such as r2 and Cohen’s d?
A. increases both (a) and (b)B. increases (a), decreases (b)
C. decreases (a), increases (b)D. decreases both (a) and (b)
14. A sample of size n = 16 produces a t statistic of 2.50.
What is the value of r2?______
15. A sample of size n = 25 is selected from a population with μ = 46. After a treatment is
administered to the sample, the sample mean is M = 48 with a sample variance of s2 = 16.
What is the size of the treatment effect as measured by Cohen’s d?
______
16. What is the critical t for a confidence interval of 80% with sample size n = 16?
______
17. What is the critical t for a one-tail t test with α = .01 and n = 15?______
18. Sample one: n = 8 and SS = 120. Sample two: n = 6 and SS = 168.
What is the pooled variance?______
For problems 19 and 20:
For an independent-measures experiment, a researcher reports the following: t(22) = 5.30,
p < .01.
19. How many individuals participated in the experiment?______
20. Was the test statistic significant?YesNo
21. An independent-measures study comparing two treatments produces a t statistic with
degrees of freedom df = 18. If the two samples have the same size, how many individuals
participated in the entire study?
A. 18B. 20C. 38D. 40
22. An independent-measures study used two samples of equal size, n = 12. If the t statistic
is t = 2.08, which of the following statements is true for a two-tail test?
A. You would reject H0 with α = .05, but not with α = .01.
B. You would reject H0 with α = .05, or with α = .01.
C. You would not reject H0 with α = .05, or with α = .01.
D. More information is needed to make a decision about H0.
23. Two samples, each with n = 9, produce an independent-measures t statistic
of t = 2.00. What is the value of r2?______
For problems 24 and 25:
You are doing a one-tail t test with α = .05. The null hypothesis is H0: μ = 180 and alternate
hypothesis H1: μ < 180. For a sample of size n = 36, mean M = 176.4, and standard deviation
sd = 12.7.
24. What is the test statistic? (Round t to 3 decimal places.)______
25. If the real mean is actually 174, what is the value of β, the measure of type II error?
______
Test 3Page 1