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Punjab (PTB) · Quarter book test · Free

2nd Year Statistics 2nd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: CHAP 12: Estimation, CHAP 13: Hypothesis Testing .

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2nd Year Statistics 2nd 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. When the null hypothesis is , the alternative hypothesis for a "less than" test of hypothesis is:

  2. 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

  3. The critical region for  when  is:

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

    1. 1.96

    2. 2.33

    3. 1.28

    4. 2.58

  5. 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

  6. 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

  7. A good scheme of education is rejected by Education Department. It is an example of:

    1. Type I error

    2. Type II error

    3. Correct decision

    4. None of these

  8. The following statistics are unbiased estimators:

    3. s2 with n - 1 as divisor

    4. All a, b and c

  9. To test hypotheses about the mean of a normal population with a known standard deviation, we can compare:

    1. The observed value of  with the critical value of 

    2. The observed value of  with the critical value of z

    3. The observed value of z with the critical value of z

    4. Either (a) or (c)

  10. A function/rule or formula that is used estimate a parameter is called:

    1. Estimate

    2. Estimator

    3. Estimation

    4. Bias

  11. For , the critical values of z for two-tailed test are equal to:

    1. -2.58 and 2.58

    2. -2.33 and 2.33

    3. -1.645 and 1.645

    4. -1.96 and 1.98

  12. The 95% confidence interval for the population proportion p is 40% to 60%, the value of the sample proportion  is:

    1. 40%

    2. 60%

    3. 50%

    4. Outside the given range

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

  1. 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 

  2. Define Type II error with example.

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

  4. Distinguish/Differentiate between simple and composite hypotheses.

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

  6. What is meant by critical region?

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

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

  9. 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.) increasing 

  10. Explain what is meant by test.

  11. If =0.10, how many intervals would be expected to contain ?

  12. Given , then find the degree of freedom for t while comparing two population means.

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

  1. 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.

  2. 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 .

  3. What is meant by estimation? Differentiate between estimator and estimate?

  4. 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.