Question

The Student Recreation Center wanted to determine what sort of physical activity was preferred by students. In a survey of 59 random students, 37 indicated that they preferred outdoor exercise over exercising in a gym. The 90% confidence interval estimating the proportion of all students at the university who prefer outdoor exercise is given by which of the following?

Question 7 options:

	1) ( 0.26933 , 0.47643 )
	2) ( 0.56416 , 0.69007 )
	3) ( 0.54644 , 0.7078 )
	4) ( -0.52357 , 0.73067 )
	5) ( 0.52357 , 0.73067 )

You are interested in getting an investment portfolio started with any extra money you make from your part time job while also going to school. While flipping through the latest edition of Money magazine, you read an article that of a survey of magazine subscribers, 154 were randomly selected and analyzed. A 90% confidence interval was constructed for the proportion of all subscribers who made money in the previous year in their investments, which was ( 0.7672 , 0.8692 ). What is the correct interpretation of this confidence interval?

Question 8 options:

	1) We are 90% confident that the proportion of all Money magazine subscribers sampled that made money in the previous year from their investments is between 0.7672 and 0.8692.
	2) We are 90% confident that the proportion of all Money magazine subscribers that made money in the previous year from their investments is between 0.7672 and 0.8692.
	3) We are certain that 90% of subscribers made between 0.7672 and 0.8692.
	4) We are 90% confident that of the 154 respondents, between 0.7672 and 0.8692 of them made more than they lost.
	5) We cannot determine the proper interpretation of this interval.

Political party affiliation is believed to be a very strong indicator of how voters will vote in Presidential Elections. You are interested in determining if voter party loyalty has changed since 1992. During the 1992 election, the proportion of self-proclaimed Republicans who voted for George H. W. Bush was 0.938. During the 2012 election, in a survey of 231 Republican voters, 184 indicated that they had voted for Mitt Romney. The 95% confidence interval for this proportion is ( 0.7446 , 0.8485 ). What is the best conclusion you can make from this information that is listed below?

Question 9 options:

	1) The confidence interval does not provide enough information to form a conclusion.
	2) We can claim that the proportion of self-proclaimed Republicans who voted in the 2012 election for their party candidate is larger than 0.938.
	3) We can claim that the proportion of self-proclaimed Republicans who voted in the 2012 election for their party candidate is smaller than 0.938.
	4) The proportion of self-proclaimed Republicans who voted for their party candidate in 2012 who changed from 0.938 is 95%.
	5) We can not conclude that the proportion of self-proclaimed Republicans who voted in the 2012 election for their party candidate differs from 0.938.

Answer 1

(7).

Answer:

Given that,

$\rightarrow$ The Student Recreation Center wanted to determine what sort of physical activity was preferred by students.

$\rightarrow$ In a survey of 59 random students, 37 indicated that they preferred outdoor exercise over exercising in a gym.

$\rightarrow$ The 90% confidence interval estimating the proportion of all students at the university

Who prefer outdoor exercise is given by which of the following:

Given that,

n = 59

x = 37

$\hat p$ = x / n = 37 / 59 = 0.627

1 - $\hat p$ = 1 - 0.627 = 0.373

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_{$\alpha$ / 2}= Z_0.05 = 1.645

Margin of error (E) :

E = Za/2 x Vp(1-P)/n)

= 1.645 x 0.627(0.373)/59

= 1.645 x 0.2338/59

= 1.645 x 70.003963

= 1.645 x 0.0629

= 0.1035

A 99% confidence interval for population proportion p is ,

P- E<P<P+E

0.627 - 0.1035< p < 0.627+ 0.1035

0.5235 < p < 0.7305

(0.5235 , 0.7305)

Answer: Option 5 (Approximately)

Note:

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