Author Question: A mayoral election race is tightly contested. In a random sample of 1200 likely voters, 636 said ... (Read 23 times)

crobinson2013 · **on:** Jul 25, 2018

A mayoral election race is tightly contested. In a random sample of 1200 likely voters, 636 said that they were planning to vote for the current mayor. Based on this sample, would you claim that the mayor will win a majority of the votes? Explain.

What will be an ideal response?

Question 2

Suppose that you know the area under the standard normal curve between 1 and 3 and the area under the standard normal curve to the left of 3.

Without further consulting a table of areas, how could you find the area under the standard normal curve to the left of 1? Explain your reasoning by using a sketch of the standard normal curve.

LegendaryAnswers · **Reply #1 on:** Jul 25, 2018

Answer to Question 1

Yes; in the sample 53 said that they were planning to vote for the current mayor and the margin of error (with 95 confidence) is smaller than 3 (it is 2.9 percentage points) so we can be 95 confident that the mayor will win more than 50 of the votes. The 95 confidence interval for the population proportion lies entirely above 50.

Answer to Question 2

The area under the standard normal curve to the left of 1 can be found by subtracting the area between 1 and 3 from the area to the left of 3.