Question

16. Confidence intervals, again Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?
a) For a given sample size, reducing the margin of error will mean lower confidence.
b) For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample.
c) For a fixed margin of error, smaller samples will mean lower confidence.
d) For a given confidence level, a sample 9 times as large will make a margin of error one third as big.

Answer 1

Answer:

Step-by-step explanation:

Confidence interval is one which has centre as mean.  The width of the interval would be 2 times margin of error.

Margin of error = Critical value * Std error/sq rt of sample

Hence if margin of error is lower for same n, then it means lower confidence level.  Option a is right

Similarly, if bigger the sample size, lower is margin of error . Hence option b is right

c) False.  Smaller samples make margin of error big and hence confidence intervals bigger.

d) If n becomes 9n, then margin of error becomes 1/3 Hence option d is right.