State whether the following statements are true or false and also give

Question

State whether the following statements are true or false and also give the reason in support of your answer:

(a) $V_{opt}\left ( \bar{X_s_t} \right )$ lies between $V_{prop}\left ( \bar{X}_{st} \right )$ and. $V_{Random}\left ( \bar{X}_{st} \right ).$ prop st Random st

(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.

(d) In a Two-way Analysis of Variance test with 5 observations per cell having 4 blocks and 4 treatments the degree of freedom for the total variation is 64.

(e) The probability of selection of a sample of n from the population by SRSWOR is 1/ N.

24 Apr 2024

Answer :

Word Count : 392

a) True. The sample mean (x̄) is an unbiased estimator of the population mean (μ), which means that the expected value of x̄ is equal to μ. Therefore, x̄ lies between the minimum and maximum values of the population.

Reason: The sample mean is calculated as the sum of all observations divided by the sample size. Since the observations are taken from the population, the ______ _____ ______ _______ _______ __________ ____.
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Gasoline A:	19	21	20	18	21	21
Gasoline B:	23	20	22	20	24	23
Gasoline C:	20	17	21	19	20	17

Treatments	Blocks
Treatments	I	II	III	IV
1	105	114	108	109
2	112	113	Y	112
3	106	114	105	109

Levels of FYM	Replications
Levels of FYM	I	II	III	IV
1	6.90	4.60	4.40	4.81
2	6.48	5.57	4.28	4.45
3	6.52	7.60	5.30	5.30
4	6.90	6.65	6.75	7.75
5	6.00	6.18	6.50	5.50
6	7.90	7.57	6.80	6.62

Village	1	2	3	4	5	6	7	8	9	10
No. of Households	35	28	20	25	30	19	10	12	18	15

Village	Ni	$\bar{X_i}$	$S_{i}^{2}$
Collage A	400	60	20
Collage B	200	120	80