IGNOU MST 4 2018 - The lifespan (in ‘000 hours) of five LED bulbs of 07 watts are a

Question

The lifespan (in ‘000 hours) of five LED bulbs of 07 watts are as follows: 40, 46, 48, 50, 42

(i) How many samples of size 2 are possible without replacement? Write them.

(ii) Compute mean of all samples of size 2 and set up the sampling distribution of the sample mean.

(iii)Compute the expected value and standard error of the sample mean.

16 Feb 2018

Answer :

Word Count : 456

Let's solve the problem step by step numerically. --- ### Given Data: The lifespan (in ‘000 hours) of five LED bulbs: \[ 40, 46, 48, 50, 42 \] --- ### (i) Number of Samples of Size 2 Without Replacement: The number of ways to choose 2 samples from 5 without replacement is: \[ \text{Total Samples} = \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5!}{2!3!} = \frac{5 \times 4}{2 \times 1} = 10 \] The 10 possible samples (pairs) are: 1. (40, 46) 2. (40, 48) 3. (40, 50) 4. (40, 42) 5. (46, 48) 6. (46, 50) 7. (46, 42) 8. (48, 50) 9. (48, 42) 10. (50, 42) --- ### (ii) Compute the Mean of All Samples and Set Up Sampling Distribution The sample mean for each pair is: \[ \bar{x} = \frac{x_1 + x_2}{2} \] | Sample | Mean \(\bar{x}\) | |---------|----------------| | (40, 46) | \(\frac{40+46}{2}

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S. No.	Test For	Name of the Test	Test Statistic	Assumptions for Applying the Test	Test Type
1	Population mean when population variance is known and population is normal	Z-test	$Z= \frac{X - \mu }{\sigma /\sqrt{n}}$	1. Sample observations should be independent. 2. The measurement scale should be at least interval scale.	Parametric Test
2	Population mean when population variance is unknown and population is normal
3	Population mean/median when the form of population is not known and sample size is small
4	Population mean/median when the form of population is not known and the data is in ordinal scale and sample

Educational attainment	Income Categories			Total
Educational attainment	Low	Middle	High	Total
No college UG PG Doctoral	32 13 43 12	20 16 51 13	23 1 60 15	75 30 154 41
Total	100	100	100	300