Question

Question 6 (1 point)

According to a survey of 786 small business participants chosen at random in the Constant Contact Small Biz Council in May of 2013, 431 of the respondents say it is harder to run a small business now than it was 5 years ago. When estimating the population proportion, what is the 90% confidence interval estimating the proportion of businesses who believe it is harder to run a business now than 5 years ago?

Question 6 options:

	1) ( 0.5306 , 0.5661 )
	2) ( 0.42246 , 0.48085 )
	3) ( 0.5256 , 0.57109 )
	4) ( 0.51915 , 0.57754 )
	5) ( -0.51915 , 0.57754 )

Question 7 (1 point)

A U.S. census bureau pollster noted that in 379 random households surveyed, 218 occupants owned their own home. What is the 99% confidence interval estimate of the proportion of American households who own their own home?

Question 7 options:

	1) ( 0.51613 , 0.63427 )
	2) ( 0.54981 , 0.60059 )
	3) ( 0.50979 , 0.6406 )
	4) ( -0.50979 , 0.6406 )
	5) ( 0.3594 , 0.49021 )

Question 8 (1 point)

You are watching a nightly news broadcast on CNN and the reporter says that a 90% confidence interval for the proportion of Americans who supported going to war in Iraq was ( 0.4073 , 0.4635 ). You also note that the footnote says this is based on a random sample performed by Gallup with 836 respondents. What is the correct interpretation of this confidence interval?

Question 8 options:

	1) We cannot determine the proper interpretation of this interval.
	2) We are 90% confident that the proportion of all Americans who supported going to war in Iraq is between 0.4073 and 0.4635.
	3) We are 90% confident that the proportion of all Americans surveyed who supported going to war in Iraq is between 0.4073 and 0.4635.
	4) We are 90% confident that of the 836 respondents, between 0.4073 and 0.4635 of them supported the decision to go to war.
	5) We are certain that 90% of Americans will be between 0.4073 and 0.4635.

Question 9 (1 point)

Based on past data, the Student Recreation Center knew that the proportion of students who prefer exercising outside over exercising in a gym was 0.836. To update their records, the SRC conducted a survey. Out of 85 students surveyed, 71 indicated that they preferred outdoor exercise over exercising in a gym. The 99% confidence interval is ( 0.7317 , 0.9389 ). Which of the following statements is the best conclusion?

Question 9 options:

	1) The proportion of students who have changed their exercise habits from 0.836 is 99%.
	2) We can not claim that the proportion of students who prefer outdoor exercise differs from 0.836.
	3) We can conclude that the proportion of students who prefer outdoor exercise is larger than 0.836.
	4) We can claim that the proportion of students who prefer outdoor exercise is smaller than 0.836.
	5) The confidence interval does not provide enough information to form a conclusion.

Answer 1

6)
sample proportion, = 0.5483
sample size, n = 786
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5483 * (1 - 0.5483)/786) = 0.01775

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.645

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5483 - 1.645 * 0.01775 , 0.5483 + 1.645 * 0.01775)
CI = (0.5191 , 0.5775)

Option (4)

7)
sample proportion, = 0.5752
sample size, n = 379
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5752 * (1 - 0.5752)/379) = 0.02539

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.576

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5752 - 2.576 * 0.02539 , 0.5752 + 2.576 * 0.02539)
CI = (0.5098 , 0.6406)

option (3)

8)

(3)

We are 90% confident that the proportion of all Americans surveyed who supported going to war in Iraq is between 0.4073 and 0.4635.

9)
We can not claim that the proportion of students who prefer outdoor exercise differs from 0.836.

Option (2)