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.
c) In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nⁿ
.d) One-way analysis of variance is a generalization of the two sample t-test.
e) If experimental error is reduced considerably and the efficiency of the design is
decreased.
f) If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
g) If one wants to convert random numbers selected from two digit numbers 00-99 to
uniformly distributed U (0, 1) variables then one has to divide them by 99.

29 Feb 2024

Answer :

Word Count : 557

Let's evaluate each statement and determine whether they are true or false, providing explanations: --- ### (c) In SRSWOR, the possible numbers of samples of size \( n \) from a population of size \( N \) if sampling is done with replacement is \( N^n \). False. - The statement refers to sampling without replacement (SRSWOR) but incorrectly describes the formula for sampling with replacement. - In Simple Random Sampling Without Replacement (SRSWOR), the number of possible samples of size \( n \) from a population of size \( N \) is: \[ \text{Total samples} = \binom{N}{n} = \frac{N!}{n!(N-n)!} \] - If sampling is done with replacement, the correct formula ______ ____ ____ _____ ______.
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Age:	22	25	22	21	22	25	24 23	22	21 20	21
22	23	25	23	24	22	24	24 21 20	23	21	22
20	20	21	22	25

Village	$N_i$	$\overline{X_i}$	$S_i^2$
Collage A	400	60	20
Collage B	200	120	80

Plot No	Group 1	Group 2	Group 3	Group 4	Group 5	Group 6
1	8	6	18	13	17	12
2	13	5	8	7	15	15
3	11	16	6	13	10	11
4	26	5	10	6	21	17
5	13	16	16	7	20	8
6	31	5	20	2	25	10

Plots	A	B	C
1	8	7	12
2	10	5	9
3	7	10	13
4	14	9	12
5	11	9	14

Machine	First shift					Second Shift
Machine	M	T	W	Th	F	M	T	W	Th	F
A	6	4	5	5	4	5	7	4	6	8
B	10	8	7	7	9	7	9	12	8	8
C	7	5	6	5	9	9	7	5	4	6
D	8	4	6	5	5	5	7	9	7	10