Question

The Pew Research Center conducted a survey about gun control in September 2019. They randomly surveyed 3,930 U.S. adults. 60% said they are in favor stricter gun laws, 28% said the laws are about right, and 12% said they are in favor of less strict laws.

a) Find a 98% confidence interval for the proportion adults in the US that are in favor of stricter gun laws. Do not make these calculations by hand. Instead, use the proper command in your graphing calculator. Write out what you entered in your calculator. (4 points)

b) Interpret your interval above in the context of this problem. (2 points)

c) If we decrease the level of confidence to 95%, will the interval be wider or narrower? (1 point)

Answer 1

Solution:

Given:

Out of randomly surveyed 3,930 U.S. adults, 60% said they are in favor stricter gun laws, 28% said the laws are about right, and 12% said they are in favor of less strict laws.

Thus  

Sample size = n = 3930

and sample proportion of U.S. adults said they are in favor stricter gun laws =

Thus x = Number of U.S. adults said they are in favor stricter gun laws =

Part a) Find a 98% confidence interval for the proportion adults in the US that are in favor of stricter gun laws.

Use following steps in TI 84 plus calculator:

Press STAT and select TESTS

Under TESTS, select 1-PropZInt

Enter given numbers:

Click on Calculate and press Enter

Thus we get confidence interval:

(0.58182 , 0.61818)

(0.5818 , 0.6182)

_{(Round final answer to specified number of decimal places)}

Thus a 98% confidence interval for the proportion of adults in the US that are in favor of stricter gun laws is between 0.5818 and 0.6182.

Part b) Interpret your interval above in the context of this problem.

We are 98% confident that the true population proportion of adults in the US that are in favor of stricter gun laws is between 0.5818 and 0.6182.

Part c) If we decrease the level of confidence to 95%, will the interval be wider or narrower?

In confidence interval for proportion:

If confidence level increases , length of confidence interval increases, that is the interval becomes wider and

If confidence level decreases, length of confidence interval decreases, that is the interval becomes narrower.

Since confidence level decreases from 98% to 95%, the interval becomes narrower.

Thus correct answer is:  narrower