Second Semester Final Exam Review Worksheet – ANSWERS
1. probability of getting results so extreme (sample results) if null is true.
2. sampling distribution is normal if population is normal; is approximately normal for large values of n
(even if population is non normal); has a mean of mu and a standard deviation of sigma divided by
root n.
3. It would be unlikely to get sample result of 54% unless true proportion is between 49% and 59%.
4. I am 90% confident that mean SAT scores of GA seniors is between 920 and 1020.
5. Type I: probability of rejecting null if null is true (alpha); Type II: probability of failing to reject
null if alternative is true (1 – power).
6. 2.05
7. mean = .23; std.dev. = .0077
8. 601
9. (.3837, .6163); I am 90% confident that Carla will make between 38.4% and 61.6% of her free
throws this season.
10. LSRL: y-hat = 60.7059 + 12.9412x; test grade is predicted to increase by about 12.9 points for each
additional hour of study; std. error of slope = 3.8275; (3.5753, 22.3071) I am 95% confident that
increase in test grade is between 3.6 and 22.3 points for each additional hour of study.
11. chi-square value = 10.54; p-value = .0051; reject null; there is a relationship
12. 29.7722
13. 9
14. 2 prop. z-test; z = 1.23 (from calc.); p-value = .219; fail to reject null; no significant difference
15. chi-square value = 4.75; p-value = .3195; fail to reject null; spinner is fair.
16. mean = 84500; std. error of mean = 4716.9906; do t-test; t = -1.1660; p-value = .2818; fail to reject
null
17. 15
18. 86%
19. matched pairs t-test (do 2-sided test); t = 2.1974; p-value = .0556; fail to reject; interval: (.4144,
4.5856)
20. (-.0639, .11385) I am 95% confident that difference in proportions between males and females who
oppose death penalty is between -.064 and .114 (interval captures 0 – likely no difference).
21. lower
22. 1-prop. z test; z = -49.17; p = 0; reject null; rate has dropped
23. t-distribution is used when sigma is unknown. It is robust (meaning reliable answers even if
distribution is nonnormal as long as sample size is large enough.) df = n – 1; Assumptions: SRS,
normal population or large sample (or graph of data shows no extremes if n = small); 2-sample t-test:
samples must be independent from distinct populations.
24. large sample – can do z-test: z=2.53;p = .0058; reject null; (t-test: t = 2.53; p=.0074; reject null).
25. 2-sample t-test; t = -2.29; p = .0222; reject null (large sample – could use z-test: z = -2.29; p = .0218)
26. t = 8.804; p = .00000018 reject null – there is a difference. Interval is (15.936, 26.064); interval
doesn’t include 0, therefore there is a difference.
27. 271
28. z-test; z = 2.1; p = .0357; reject null; there is a difference
29. 1-prop. z test; z = -1.6407 (from calc); p = .1009; fail to reject null; no difference