Question

Which of the following estimates at a 95% confidence level most likely comes from a small sample

Answer 1

Answer:

Answer is c

Step-by-step explanation:

In hypothesis testing whether to accept or reject null hypothesis, normally we find one method as using confidence interval.  If the test statistic lies within confidence interval, we accept otherwise we reject.

For arriving confidence intervals we add and subtract margin of error from the mean we use in null hypothesis.

Margin of error = std error * critical value of test (Z or t etc)

For the same std deviation, std error = std dev/sq rt of sample size

Thus std error is inversely proportional to the square root of sample size.

If n becomes larger, std error becomes smaller and vice versa.

So margin of error increases for smaller sample size.

Since we have to select confidence level from a small sample, we have to select one which has the greatest margin of error=18

Hence answer is

c)  71%(+/-18%)