Statistics Chapter 7

Question

Suppose that the duration of a particular type of criminal trial is known to have a mean of 21 days and a standard deviation of 7 days. We randomly sample 9 trials.

Ninety percent of the total of 9 of these types of trials will last at least how long? (Round your answer to two decimal places.)

Answer 1

Hi Priscilla,

This is a one-sided confidence interval, which is rare, but we can calculate it. You have known population standard deviation, so you can use z. Initial formula is same as for two-sided:

CI=x-bar +/- z*SE

Let's break this down

x-bar=sample mean

z*=z-critical value, explained below

SE=standard error, which has its own calculation

SE=s/sqrt(n)

Let's calculate that first:

s=7

n=9

SE=7/sqrt(9)

SE=7/3

Now, for this problem, we have:

x-bar=21

SE=7/3

But we still need to compute z*, the z-critical value. We have a 90% confidence level here and this is one-sided--the problem asks only for the lower bound, so we can look in the interior of the z-table for 0.90. The closest z-score to this is 1.28, so:

x-bar=21

SE=7/3

z*=1.28

CI=21 - (7/3)(1.28)

CI=21-2.99

CI=18.01, infinity

Lower bound is 18.01 days. I hope this helps.