In a survey of 3,778 travelers, 1,486 said that location was very important for
ID: 3156932 • Letter: I
Question
In a survey of 3,778 travelers, 1,486 said that location was very important for choosing a hotel and 1, 214 said that reputation was very important in choosing an airline. Complete parts (a) through (c) below. Construct a 95% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel. LE pi LE (Round to four decimal places as needed.) Construct a 95% confidence interval estimate for the population proportion of travelers who said that reputation was very important in choosing an airline. LE pi LE (Round to four decimal places as needed.) 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)? 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). 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). 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). 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). Which of the following is the best summary of the information derived from (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). 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). 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). 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).Explanation / Answer
a.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Hotel(x)=1486
Sample Size(n)=3778
Sample proportion = x/n =0.3933
Confidence Interval = [ 0.3933 ±Z a/2 ( Sqrt ( 0.3933*0.6067) /3778)]
= [ 0.3933 - 1.96* Sqrt(0.0001) , 0.3933 + 1.96* Sqrt(0.0001) ]
= [ 0.3777,0.4089]
b.
Airlines(x)=1214
Sample Size(n)=3778
Sample proportion = x/n =0.3213
Confidence Interval = [ 0.3213 ±Z a/2 ( Sqrt ( 0.3213*0.6787) /3778)]
= [ 0.3213 - 1.96* Sqrt(0.0001) , 0.3213 + 1.96* Sqrt(0.0001) ]
= [ 0.3064,0.3362]
c.
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)
d.
One can be 95% confident that the population proportion of all travelers who said that reputation was very important in choosing an airline ties within the interval in (b).
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