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Unformatted text preview: ark of the College Entrance Examination Board. AP® Statistics 2000 ─ Scoring Guidelines
Question 4
Solution
a. part 1: States a correct pair of hypotheses
Ho: µW = µN
Ho: µW  µN = 0
OR
Ha: µW ≠ µN
Ha: µW  µN ≠ 0
where µW is the mean mental skill score for babies who used walkers and
µN is the mean for those who did not. Nonstandard notation must be
__ ∧ explained. Hypotheses about statistics (e.g. x or p ) are unacceptable.
part 2: Identifies a correct test (by name or by formula), and checks appropriate
assumptions.
Note: Problem states that samples are random samples, so this does not need to be
addressed in the assumptions.
Independent samples t test. Assumptions: large sample or normal population
distributions. Check: OK, because, for example, n1&n2>30.
OR
Pooled t test. Assumptions: large samples or normal population distributions,
equal population standard deviations. Checks: OK because, for example,
n1&n2>30 and s1≈s2.
OR
Independent samples z test. Assumptions: large samples. Check: OK because,
for example, n1&n2>30.
part 3: Correct mechanics, including value of test statistic, df (if appropriate), and Pvalue or rejection region (except for minor arithmetic errors)
• For independent samples t test:
__ t= __ xW − x N = 113 − 123 = − 10 = −3.8468
2
2
6.7576
12 2 15 2
sW s N
+
+
54
55
nW n N
(Calculator: t = 3.846843677)
df = 102.828 (OK to use 102), Pvalue = .0002
OR conservative df = 54  1 = 53, Pvalue = 2(.00016)=.00032
OR using tables (for either df) Pvalue < 2(.0005) = .001
• For pooled t test: sp = 13.597, t = 3.839, df = 107, Pvalue = .0002
(or < .001 from tables) • For independent samples z test, z = 3.8468, Pvalue = .0001
(or <2(.0002) = .0004 from tables) Copyright © 2000 College Entrance Examination Board and Educational Testing Service. All rights reserved.
AP is a registered trademark of the College Entrance Examination Board. AP® Statistics 2000 ─ Scoring Guidelines
Question 4 continued
part 4: Stating a correct conclusion in the context of the problem, using the resu...
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This note was uploaded on 09/06/2013 for the course MATH AP Statist taught by Professor Mosby during the Spring '13 term at Silverton High School, Silverton.
 Spring '13
 Mosby
 Statistics, AP Statistics

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