Question

Listed below are weights (in hectograms) of a simple random sample of girls at birth, based on data from National Center for Health Statistics. Assume that the birth weights of girls are normally distributed with σ ​=3.0 hecgtograms. 33,28,33,37,31,32,31,28,34,28,33,26,20,31,28

A) use the sample data to construc a 96% confidence interval for the true mean birth weight of girls.

B) use the sample data to construct 90% confidence interval for the true mean birth weight of girls.

C) how do the intervals in part a and b compare ? if you increase the confidence level, what happens to the confidence interval?

Answer 1

Here σ ​=3.0 so we will use z distribution to find confidence interval

For the given data

A. For 96% CI, z value is 2.054, as

So Margin of Error is

So CI is

B. For 90% CI, z value is 1.645

So Margin of Error is

So CI is

C. From a and b, we see that as we decrease the confidence level width decreases

If we increase the CI level width will increase.