#### Sampling Techniques and Statistical Inference Model Question Paper

12th Standard EM

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Time : 01:30:00 Hrs
Total Marks : 50
9 x 1 = 9
1. A ________ may be finite or infinite according as the number of observations or items in it is finite or infinite.

(a)

Population

(b)

census

(c)

parameter

(d)

none of these

2. A finite subset of statistical individuals in a population is called __________

(a)

a sample

(b)

a population

(c)

universe

(d)

census

3. Any statistical measure computed from sample data is known as ____________

(a)

parameter

(b)

statistic

(c)

infinite measure

(d)

uncountable

4. In ___________ the heterogeneous groups are divided into homogeneous groups.

(a)

Non-probability sample

(b)

a simple random sample

(c)

a stratified random sample

(d)

systematic random sample

5. Errors in sampling are of

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

6. An estimator is a sample statistic used to estimate a

(a)

population parameter

(b)

biased estimate

(c)

sample size

(d)

census

7. An estimator is said to be __________ if it contains all the information in the data about the parameter it estimates.

(a)

efficient

(b)

sufficient

(c)

unbiased

(d)

consistent

8. A ________ is a statement or an assertion about the population parameter.

(a)

hypothesis

(b)

statistic

(c)

sample

(d)

census

9. Type II error is

(a)

Accept H0 when it is wrong

(b)

Accept H0 when it is true

(c)

Reject H0 when it is true

(d)

Reject H0 when it is false

10. 8 x 2 = 16
11. What is population?

12. What is statistic?

13. What is standard error?

14. State any three merits of stratified random sampling.

15. What is an estimator?

16. A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant?

17. Write short note on sampling distribution and standard error.

18. The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15 ? (Test at 5% level of significance)

19. 5 x 3 = 15
20. Using the following random number table (Kendall-Babington Smith)

 23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44 05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43 14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34 38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95 97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13

Draw a random sample of 10 four- figure numbers startingfrom 1550 to 8000.

21. A server channel monitored for an hour was found to have an estimated mean of 20 transactions transmitted per minute. The variance is known to be 4. Find the standard error.

22. Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

23. The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?

24. A sample of 100 students is chosen from a large group of students. The average height of these students is 162 cm and standard deviation (S.D) is 8 cm. Obtain the standard error for the average height of large group of students of 160 cm?

25. 2 x 5 = 10
26. An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for the 50 cars was 10 km per litre with a standard deviation of 3.5 km per litre. Test at 5% level of significance, whether the claim of the new car petrol consumption is 9.5 km per litre on the average is acceptable.

27. The wages of the factory workers are assumed to be normally distributed with mean and variance 25. A random sample of 50 workers gives the total wages equal to Rs. 2,550. Test the hypothesis $\mu$=52, against the alternative hypothesis $\mu$=49 at 1% level of significance.