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Punjab (PTB) · Half book test · Free

2nd Year Statistics First half Book Paper

50 marks · 1 hour 30 minutes · 35 questions. Covers: 4 chapters (CHAP 10: Normal Distribution to CHAP 13: Hypothesis Testing ).

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2nd Year Statistics First half Book Paper

2nd Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 50Time: 1 hour 30 minutes

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

  1. A sample of size n is called a small sample if n is:

    1. Less than 30

    2. Greater than or equal to 30

    3. Equal to 30

    4. Less than or equal to 30

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

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

    1. Increased

    2. Decreased

    3. Fixed

    4. Small

  4. When the null hypothesis is , the alternative hypothesis for a "less than" test of hypothesis is:

  5. For , the critical value for two tailed test is equal to:

    1. 1.96

    2. 2.33

    3. 1.28

    4. 2.58

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

    1. 0.7979

    2. 0.6745

    3. -0.6745

    4. -0.7979

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

    1. Finite population

    2. Infinite population

    3. Target population

    4. Sampled population

  8. The critical region for  when  is:

  9. For small sample size and unknown population standard deviation the confidence interval for the population mean  is based on:

    1. The normal distribution

    2. The "" distribution

    3. The binomial distribution

    4. The hypergeometric distribution

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

    1. Not equal

    2. Positive

    3. Equal

    4. None

  11. 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

  12. For a particular hypothesis test,  and . The power of the test is equal to

    1. 0.14

    2. 0.90

    3. 0.95

    4. 0.25

  13. The following statistics are unbiased estimators:

    3. s2 with n - 1 as divisor

    4. All a, b and c

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

    1. 0 & 3

    2. 3 & 0

    3. 0 & 1

    4. 1 & 3

  15. 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:

Q2. Short questions (Attempt any 10 of 15 · 10 × 2 = 20)

  1. Define Type II error with example.

  2. When setting a two-sided  confidence interval for , based on a random sample of size n from a normal population, how the following change will affect the length of the confidence interval for ; (Assume all other quantities remain fixed.) decreasing 

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

  4. 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?

  5. Distinguish/Differentiate between simple and composite hypotheses.

  6. Specify the estimator and the estimate in the following: A sample of 35 students gave an average height of 62 inches.

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

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

  9. What is meant by critical region?

  10. Specify the estimator and the estimate in the following: A sample of 30 houses showed an average consumption of electricity as 65 units.

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

  12. If  find. (i) P(|Z| < 3)

  13. How do you select a best test of a statistical hypothesis?

  14. How would you construct a  confidence interval for the binomial parameter p?

  15. Define sampling.

Q3. Long questions (Attempt any 3 of 5 · 3 × 5 = 15)

  1. Two samples of sizes 400 and 300 having means 52 and 50 are drawn from the same population of s.d. 3. Test the hypothesis  vs. . Use .

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

  3. 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 .

  4. Give that:  and assuming that the two samples were randomly selected from two normal populations in which  (but unknown), calculate an 80% confidence interval for the difference between the two population means.

  5. The lives in hours of 10 bulbs were found to be 1250, 1187, 1201, 1300, 1100, 1050, 1240, 1150, 1075, 1260. Test the hypothesis that the mean life in the population of bulbs is 1200 hours at (i) 5% (ii) 1% level of significance.