Rajesh calculated 95% confidence level. What does he mean by that?
(A) He can be 95% confident that his sample will include the population parameter.
(B) He can be 95% confused that his sample will include the population parameter.
(C) He can be 5% confident that his sample will not include the population parameter.
(D) He can be 5% confident that his sample will include the population parameter.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (C) only
A 95% confidence level means that the method used to build the confidence interval from a sample captures the population parameter in 95% of all possible samples. So for the interval worked out from his sample, Rajesh can be 95% confident that it includes the parameter, and there is a 5% chance that it does not. In the statements, “his sample will include the parameter” refers to the interval computed from his sample.
So the confidence of including the parameter is 95%, and the chance of not including it is 100% − 95% = 5%.
Checking the statements
(A) He can be 95% confident that his sample will include the population parameter. — Correct. This is the meaning of the 95% level.
(B) He can be 95% confused that his sample will include the population parameter. — Incorrect. The level measures confidence, not confusion.
(C) He can be 5% confident that his sample will not include the population parameter. — Correct. The remaining 5% is the chance of missing the parameter.
(D) He can be 5% confident that his sample will include the population parameter. — Incorrect. The confidence of including it is 95%, not 5%.