Question

In a survey of 3,827 ​travelers, 1,459 said that location was very important for choosing a hotel and 1,175 said that reputation was very important in choosing an airline. Complete parts ​(a) through​ (c) below.

a. Construct a 95​% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel.

b. Construct a 95​% confidence interval estimate for the population proportion of travelers who said that reputation was very important in choosing an airline.

c. Write a short summary of the information derived from​ (a) and​ (b) Which of the following is the best summary of the information derived from​ (a)?

A.One can be 95​% confident that the sample proportion of all travelers who said that location was very important for choosing a hotel lies within the interval in​ (a).

B.One can be 95​% confident that the population proportion of all travelers who said that location was very important for choosing a hotel lies within the interval in​ (a).

C.There is a 95​% probability that the sample proportion of all travelers who said that location was very important for choosing a hotel lies within the interval in​ (a).

D.There is a 95% probability that the population proportion of all travelers who said that location was very important for choosing a hotel lies within the interval in​ (a).

Which of the following is the best summary of the information derived from​ (b)?

A.One can be 95​% confident that the population proportion of all travelers who said that reputation was very important in choosing an airline lies within the interval in​ (b).

B.One can be 95​% confident that the sample proportion of all travelers who said that reputation was very important in choosing an airline lies within the interval in​ (b).

C.There is a 95​% probability that the sample proportion of all travelers who said that reputation was very important in choosing an airline lies within the interval in​ (b).

D.There is a 95​% probability that the population proportion of all travelers who said that reputation was very important in choosing an airline lies within the interval in​ (b).

Answer 1

(a)

n = 3827

p = 1459/3827 = 0.3812

q = 1- p = 0.6188

SE =

= 0.05

From Table critical values of Z = 1.96

Confidence Interval:

0.3812 (1.96 X 0.0079)

= 0.3812 0.0154

= ( 0.3658 , 0.3966)

So,

Confidence interval:

0.3658 < P < 0.3966

(b)

n = 3827

p = 1175/3827 = 0.3070

q = 1- p = 0.6930

SE =

= 0.05

From Table critical values of Z = 1.96

Confidence Interval:

0.3812 (1.96 X 0.0075)

= 0.3812 0.0146

= ( 0.3666 , 0.3958)

So,

Confidence interval:

0.3666 < P < 0.3958

(c)

Correct option:

D. There is 95% probability that the population proportion of all travelers who said that location was very important in choosing an airline lies within the interval in (a).

(d)

Correct option:

D.    There is 95% probability that the population proportion of all travelers who said that reputation was very important in choosing an airline lies within the interval in (b).