Question

Lisa decides that she wants to know the 85% confidence interval for a population mean despite originally setting out to find the 90% confidence interval. How will this affect the width and the margin of error of her confidence interval for a population mean? Assume that the population standard deviation is unknown and the population distribution is approximately normal.

Select your answer from the choices below.

1. The width will decrease, and the margin of error will increase.
2. The width will decrease, and the margin of error will decrease.
3. The width will increase, and the margin of error will increase.
4. The width will increase and the margin of error will decrease

Answer 1

Solution:

Assume that the population standard deviation is unknown and the population distribution is approximately normal.

So , we use t distribution.

As confidence level decreases , then the critical t value also decreases .(assuming same sample size)

Then the margin of error also decreases . So that the interval becomes narrower.

1st confidence level is 90%

2nd confidence level is 85%

So , correct option is

The width will decrease, and the margin of error will decrease.