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Punjab (PTB) · Quarter book test · Free

2nd Year Statistics 1st Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: CHAP 10: Normal Distribution , CHAP 11: Sampling Techniques And Sampling Distribution .

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2nd Year Statistics 1st Quarter Book Paper

2nd Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. In a normal distribution , Q1 is equal to:

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

    1. Increased

    2. Decreased

    3. Fixed

    4. Small

  3. In a standard normal distribution, Q1 is equal to:

    1. 0.7979

    2. 0.6745

    3. -0.6745

    4. -0.7979

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

    1. Finite population

    2. Infinite population

    3. Target population

    4. Sampled population

  5. In normal distribution mean, median and mode are:

    1. Not equal

    2. Positive

    3. Equal

    4. None

  6. 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

  7. In a normal distribution, the value of  are respectively:

    1. 0 & 3

    2. 3 & 0

    3. 0 & 1

    4. 1 & 3

  8. 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:

  9. The number of parameters of normal distribution is:

    1. One

    2. Two

    3. Three

    4. Four

  10. 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

  11. In a normal distribution  of the area lies between the limits.

  12. 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

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

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

  2. The grade-point averages of 300 college freshmen follow approximately a normal distribution with a mean of 2.1 and a standard deviation of 0.8. How many of these freshmen would you expect to have a score between 2.5 and 3.5 inclusive if the point averages are computed to the nearest tenth?

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

  4. If the random variable Z has the standard normal distribution, find. (i) P(Z>1.96)

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

  6. If  find. (i) P(|Z| < 3)

  7. Define sampling.

  8. If  find. (i) P(|Z| < 1)

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

  10. If , find a if: (i) P(Z > a) = 0.025

  11. 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.

  12. In a normal distribution  and P(25 < X < 55)=0.8662. Find P(20 < X < 60).

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. Find the value of X which corresponds to a standardized value of -2.05 and 0.86 for the following distribution. (i) 

  2. 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 .

  3. The continuous random variable X is normally distributed with mean  and standard deviation . Given that P(X < 53)=0.04 and P(X <65) =0.97. Find the inter quartile range of the distribution.

  4. 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.