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Punjab (PTB) · Chapter test · Free

2nd Year Statistics Chapter 2 TestSampling Techniques And Sampling Distribution

30 marks · 40 minutes · 21 questions. Covers: CHAP 11: Sampling Techniques And Sampling Distribution .

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2nd Year Statistics Chapter 2 Test

2nd Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. The standard error increase when the sample size is:

    1. Increased

    2. Decreased

    3. Fixed

    4. Small

  2. The population about which some information is required is called:

    1. Finite population

    2. Infinite population

    3. Target population

    4. Sampled population

  3. If the sampling distribution of is normal, the interval includes:

    1. 68.27% of the sample means

    2. 95% of the sample means

    3. 95.45% of the sample means

    4. 90% of the sample means

  4. If samples of size n are drawn without replacement from a population of size N with mean  and variance , the standard error of the sample mean  is:

  5. The central limit theorem assures us that the sampling distribution of the mean:

    1. Is always normal

    2. Is always normal for large sample sizes

    3. Approaches normality as sample size increases

    4. Appears normal only when N is greater than 1000

  6. The errors which arise due to processing of data and faulty sampling frame is called:

    1. Sampling error

    2. Non-sampling error

    3. Standard error

    4. Random error

  7. A value calculated from the sample is called a:

    1. Parameter

    2. Statistic

    3. Mean

    4. Proportion

  8. Suppose you are performing stratified random sampling on a particular population and have divided it into strata of different sizes. How can you now make your sample selection?

    1. Select at random an equal number of elements from each stratum

    2. Draw equal numbers of elements from each stratum and weight the results

    3. Draw numbers of elements from each stratum proportional to their weights in the population

    4. Both (b) and (c) but not (a)

  9. If N  is the size of the population and n is the size of the sample, then sampling fraction is:

    2. Sample size + population size

    4. (a) and (b) but not (c)

  10. A border petrol check point that stops every tenth van is using:

    1. Simple random sampling

    2. Systematic sampling

    3. Stratified sampling

    4. Complete enumeration

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Given n = 9, and , find and .

  2. Explain the properties of the sampling distribution of a mean.

  3. If , N = 6, n = 2 then find for sampling distribution without replacement.

  4. Define sampling.

  5. What is the difference between bias and sampling error?

  6. Given the following population distribution

    x 3 4 5
    f(x) 1/4 2/4 1/4

    Find  when n = 2 without replacement  is the proportion of even numbers.

  7. A family has 5 children with 3 boys (B) and 2 girls (G) as given below.

    Child I II III IV V
    Sex B G G B B

    Find the proportion of boys in the population.

  8. If , population variance , then find "n" for sampling with replacement.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. A finite population consists of five values 2, 4, 6, 8 and 10. Take all possible samples of size 2 which can be drawn with replacement from this population. Assuming the 25 possible samples equally likely, construct the sampling, distribution of sample means and sample variances and find the mean of these distributions. Calculate the mean and variance of the population and verify that: (i)  (ii)  where  and .

  2. Draw all possible samples of two letters each without replacement from the letters of the word "KASHMIR". Find proportion of vowel letters in each sample and make a sampling distributions of proportion compute the mean and standard error of sampling distribution and compute the results.

  3. If the size of the simple random sample from an infinite population is 55, the variance of sample mean is 27, what must be the standard error of sample mean if n = 165?