tate whether the following statements are True or False. Give reason i

Question

tate whether the following statements are True or False. Give reason in support of your answer:

(a) If the probability of non rejection of Ho when H, is true is 0.4 then power of the test will be 0.6.

(b) If T₁ and T₂ are two estimators of the parameter & such that Var(T₁)-1/n and Var(T₂)n then T, is more efficient than T₂.

(d) If the level of significance is the same, the area of the rejection region in a two-tailed test is less than that in a one-tailed test.

(e) Non parametric tests are more powerful than the parametric tests.

20 Feb 2025

Answer :

Word Count : 226

(a) True. The power of a test is given by \( 1 - \beta \), where \( \beta \) is the probability of failing to reject \( H_0 \) when \( H_1 \) is true. Given that \( \beta = 0.4 \), the power of _____ ________ _______ ______ __________ __________ ____ _____ ___ _________ _____ __________.
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Worker A	19	22	24	27	24	18	20	19	25
Worker B	26	37	40	35	30	40	26	30	35	45

	Developing Section	Rest of the City
Sample size	50	100
Number favoring proposa	38	65

Campaign
1	2	3
0.33	0.28	0.21
0.29	0.41	0.30
0.21	0.34	0.26
0.32	0.39	0.33
0.25	0.27	0.31

Student	With Imagery	Without Imagery	Student	With Imagery	Without Imagery
1	20	5	11	17	8
2	24	9	12	20	16
3	20	5	13	20	10
4	18	9	14	16	12
5	22	6	15	24	7
6	19	11	16	22	9
7	20	8	17	25	21
8	19	11	18	21	14
9	17	7	19	19	12
10	21	9	20	23	12

	Region
	1	2
Sample size	100	100
Sample mean	2.4	3.1
Sample variance	1.44	2.64