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Chapter 16
1. Using the formula k(k 1)=2, determine the number of t tests required to make all possible pairwise comparisons for each of the following conditions: (a) k ¼ 2 (b) k ¼ 4 (c) k ¼ 6 (d) k ¼ 7


a.) 2*1/2 = 1

b.) 4*3/2 = 6

c.) 6*5/2 = 15

d.) 7*6/2 = 21



will post shortly one by one the answer

2. A graduate student wishes to compare the high school grade-point averages (GPAs) of males and females. He identifies 50 brother/sister pairs, obtains the GPA for each individual, and proceeds to test H0: mmales mfemales ¼ 0. Are the methods discussed in this chapter appropriate for such a test? (Explain.)



Answer:

Yes since this can be tested using t test for independent samples




4. Assume H0: m1 m2 ¼ 0 is true. What are the three defining characteristics of the sampling distribution of differences between means?



Answer:

It is normally distributed

Its mean of difference is equal to m1 - m2

Its standard devation of S(diff) / sqrt n






8. Does familiarity with an assessment increase test scores? You hypothesize that it does. You identify 11 fifth-grade students to take a writing assessment that they had not experienced before. Six of these students are selected at random and, before taking the assessment, are provided with a general overview of its rationale, length, question format, and so on. The remaining five students are not given this overview. The following are the scores (number of points) for students in each group: overview provided : 20; 18; 14; 22; 16; 16 no overview provided : 11; 15; 16; 13; 9 (a) Set up H0 and H1 (b) Perform the test (a ¼ :01). (c) Draw your final conclusions.





Answer:

a.)



Ho:

µ1 = µ2



H1:

µ1 ≠ µ2



b.)



Critical t values

t = ± 3.2498







Test Statistic:





t = 2.7633



Decision:



Do not reject Ho





c.)



Conclusion:



The population means are not significantly different.




9. An educational psychologist is interested in knowing whether the experience of attending preschool is related to subsequent sociability. She identifies two groups of first graders: those who had attended preschool and those who had not. Then each child is assigned a sociability score on the basis of observations made in the classroom and on the playground. The following sociability results are obtained: Attended Preschool Did Not Attend Preschool n1 ¼ 12; SX1 ¼ 204; SS1 ¼ 192 n2 ¼ 16; SX2 ¼ 248; SS2 ¼ 154 (a) Set up the appropriate statistical hypotheses. (b) Perform the test (a ¼ :05). (c) Draw final conclusions.



Answer:

a.)



Ho:

µ1 = µ2



H1:

µ1 ≠ µ2



b.)



Critical t values

t = ± 2.0556







Test Statistic:





t = 1.0767



Decision:



Do not reject Ho





c.)



Conclusion:



The population means are not significantly different.




12. Parametric statistical tests are tests that are based on one or more assumptions about the nature of the populations from which the samples are selected. What assumptions are required in the t test of H0: m1 m2 ¼ 0?

Answer:

Normality

Independence of samples

Equality of variance





16. The director of Academic Support Services wants to test the efficacy of a possible intervention for undergraduate students who are placed on academic probation. She randomly assigns 28 such students to two groups. During the first week of the semester, students in Group 1 receive daily instruction on specific strategies for learning and studying. Group 2 students spend the same time engaged in general discussion about the importance of doing well in college and the support services that are available on campus. At the end of the semester, the director determines the mean GPA for each group: Group 1 (Strategy Instruction) Group 2 (General Discussion) n1 ¼ 14; X1 ¼ 2:83; s1 ¼:41 n2 ¼ 14; X2 ¼ 2:26; s2 ¼ :39 (a) Set up the appropriate statistical hypotheses. (b) Perform the test (a ¼ :05). (c) Draw final conclusions



Answer:

a.)



Ho:

µ1 = µ2



H1:

µ1 ≠ µ2



b.)



Critical t values

t = ± 2.0556







Test Statistic:





t = 3.769



Decision:



Reject Ho





c.)



Conclusion:



The population means are significantly different.






Chapter 15
2. (a) How can the use of matched pairs be of help statistically? (b) What one single value can you compute from the results of a matched-pairs investigation that will tell you the degree to which the matching has helped?



Answer:

a.) It can be of help for paired or dependent samples like pretest and posttest, or same set subjects that are measured twice.

b.) Mean of difference and its standardized value.


12. You wish to see whether students perform differently on essay tests and on multiple choice tests. You select a sample of eight students enrolled in an introductory biology course and have each student take an essay test and a multiple-choice test. Both tests cover the same unit of instruction and are designed to assess mastery of factual knowledge. (Half the students take the essay test first; the remaining half take the multiple-choice test first.) The results are as follows: Student A B C D E F G H Essay: 43 39 44 47 30 46 34 41 Multiple choice: 45 33 46 49 28 43 36 37 Using the direct-difference method: (a) Set up the statistical hypotheses. (b) Compute D, SSD, and sD . (c) Perform the test (a ¼ :05). (d) Draw final conclusions.



Answer:

a.)



Null Hypothesis:

Students do not perform differently on essay tests and on multiple choice tests

Ho: µ_d = 0



Alternative Hypothesis:

Students do perform differently on essay tests and on multiple choice tests

H1: µ_d ≠ 0

b.)

		difference
43	45	-2	4
39	33	6	36
44	46	-2	4
47	49	-2	4
30	28	2	4
46	43	3	9
34	36	-2	4
41	37	4	16
sum		7	81
D		0.8750
		3.2705

Dbar = 0.8750

SSD = 81

S_d = 3.2705


c.)

Null Hypothesis:

Students do not perform differently on essay tests and on multiple choice tests

Ho: µ_d = 0



Alternative Hypothesis:

Students do perform differently on essay tests and on multiple choice tests

H1: µ_d ≠ 0

Critical t values:

T = ± 2.3646



Computed t value:

T = (Md - µd) / (sd / Ön)

= (0.8750 - 0) / (3.2705 / Ö8)

= 0.7567

Decision:

Do not reject Ho:



Conclusion:

Students do not perform differently on essay tests and on multiple choice tests or Ho: µ_d = 0 at alha = 0.05 (2 tailed)





Chapter 16
1. Using the formula k(k 1)=2, determine the number of t tests required to make all possible pairwise comparisons for each of the following conditions: (a) k ¼ 2 (b) k ¼ 4 (c) k ¼ 6 (d) k ¼ 7

Answer:

a.) 2*1/2 = 1

b.) 4*3/2 = 6

c.) 6*5/2 = 15

d.) 7*6/2 = 21



7. Study the following ANOVA summary, and then provide the missing information for the cells designated a-f: Source SS df MS F p Between-groups (a) 3 (b) (c) (d) Within-groups 64 (e) (f) Total 349 19

SOURCES	SS	DF	MS	F COMPUTED	P value
between	19	3	6.3333	1.2283	0.307
within	330	64	5.1563
TOTAL	349	67

9. (a) How many groups are there in Problem 7? (How do you know?) (b) What is the total sample size in Problem 7? (How do you know?) (c) How many groups are there in Problem 8? (How do you know?) (d) What is the total sample size in Problem 8? (How do you know?)

Answer:

a.) 4

b.) 68 (the formula is n - 1)

for c and d, problem 8 is missing, please provide problem number 8, thanks

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