Quiz Space

Statistics for Data Science II · Quiz 2 · 16 Mar 2025 · January 2025 term

Question 6: How does the variance of the sample mean change?

Question 6

+2 marksOne correct option

Wires produced from a factory have a mean breaking strength of 50 kilograms with a standard deviation of 4 kilograms. In a statistical study of breaking strength of these wires, suppose the sample size is increased from 81 to 144.
Based on the above data, answer the given subquestions.

How does the variance of the sample mean change?

  1. A

    Variance is reduced from 0.049 to 0.027

  2. B

    Variance is reduced from 0.198 to 0.111

  3. C

    Variance is increased from 0.111 to 0.198

  4. D

    Variance remains the same.

Show answer

Correct answer

  • B

    Variance is reduced from 0.198 to 0.111

See the whole paperTake it as a mock test

Question 6 of 16 in the IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term (IIT M DIPLOMA AN EXAM QDD2 16 Mar 2025). It carries 2 marks.

More questions from this paper

  1. Q1Figure question
  2. Q2Figure question
  3. Q3Figure question
  4. Q4Figure question
  5. Q5How does the expected value of the sample mean change?
  6. Q7Find the value of E[X]. Enter the answer correct to two decimal places
  7. Q8What is the value of Var(X)? Enter the answer correct to two decimal places.
  8. Q9Find the value of k.
  9. Q10Based on the above data, answer the given subquestions.
  10. Q11Which of the following option(s) is(are) correct ?
  11. Q12Using Chebyshev’s inequality, find a lower bound for P(|Y −0.5| \< 0.6). Enter the answer correct to three decimal plac…
  12. Q13Based on the above data, answer the given subquestions.
  13. Q14Based on the above data, answer the given subquestions.
  14. Q15Which of the following options is an acceptable approximate model for S as per the Central Limit Theorem?
  15. Q16Using the Central Limit Theorem, find an approximate probability that the total number of heads, S, lies between 48 and…