Question

PLEASE SHOW WORK

Suppose that in a two-tailed hypothesis test you calculated a Z statistic of -1.75. What is your p-value? And how would you conclude if α = 5%?
P-value = 0.0401. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should not be rejected at the 5% level
P-value = 0.0402. H0 should be rejected at the 5% level      
None of the above statements is correct

For this and the next 3 questions. A journal article by Kashima et al describes research with parents of mentally retarded children in which a media-based program presented, primarily through videotapes and instructional manuals, information on self-help skill teaching. As part of the study, 17 families participated in a training program led by experienced staff members of a parent training project. Before and after the training program, the Behavioral Vignettes Test was administrated to the primary parents in each family. The test assesses knowledge of behavior modification principles. A higher score indicates greater knowledge. The following are the pre- and post-training scores made by the primary parent on the test. Can we conclude, on the basis of these data, that the training program INCREASES KNOWLEDGE of behavior modification principles? To begin, what is the correct statement of hypothesis for this test? [Source: "Media-based Versus Professionally Led Training Parents of 'V'êÈÜ«Mentally retarded Children," American Journal on Mental Retardation, 93 (1988), 209-217]

Pre	Post
7	11
6	14
10	16
16	17
8	9
13	15
8	9
14	17

H0: σ2A ≥ σ2B; H1: σ2A < σ2B
H0: μA = μB; H1: μA ≠ μB  
H0: μD ≥ 0; H1: μD < 0
H0: μD ≤ 0; H1: μD > 0      
H0: μD = 0; H1: μD ≠ 0
None of the above

From your computer output, what is the correct p-value for this test?

		6.1110
		Less than 0.01
		2.5835
		2.9208
		More than 0.05
		None of the above

From your computer output, what is the correct critical value for this test - at the 0.01 level of significance?

		6.111
		Less than 0.01
		2.5835
		2.9208
		More than 0.05
		None of the above

What is your decision? How do you conclude

		Do not reject H0 . There is no evidence of knowledge gain
		Reject H0. There is evidence of knowledge improvement at the 1% level of significance
		Reject H0. The calculated statistic is less than the critical value at the 1% level of significance
		Do not reject H0. The calculated statistic is greater than the critical value at the 1% level of significance
		None of the above

Answer 1

Ans:

1)

p-value(2 tailed)=2*P(z<-1.75)=2*NORMSDIST(-1.75)=0.0802

P-value = 0.0802. H0 should not be rejected at the 5% level.

2)

	Pre	Post	d
1	7	11	4
2	6	14	8
3	10	16	6
4	16	17	1
5	8	9	1
6	13	15	2
7	8	9	1
8	14	17	3
		d-bar=	3.25
		sd=	2.605

H0: μD ≤ 0; H1: μD > 0  

test statistic:

t=(3.25-0)/(2.605/sqrt(8))

t=3.529

df=8-1=7

p-value=tdist(3.529,7,1)=0.0048

p-value is Less than 0.01

critical t value=2.998

Reject H_0. There is evidence of knowledge improvement at the 1% level of significance