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In: Statistics and Probability

In a survey of 3929 ​travelers, 1431 said that location was very important for choosing a...

In a survey of 3929 ​travelers, 1431 said that location was very important for choosing a hotel and 1222 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.

Solutions

Expert Solution

Total number of travelers = n = 3929

x1 = total number of travelers who said that location was very important for choosing a hotel =1431

x2 = total number of travelers who said that reputation was very important in choosing an airline = 1222

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

The formula of confidence interval for the population proportion is as follow:

Where E is the margin of error:

The formula of E is as follow:

Here   = x1 / n = 1431 / 3929 = 0.3642

Let's find the value of   in excel:

Plug all the required values in the formula of E, we get

So that ,

Lower limit = - E = 0.3642 - 0.0150= 0.3492

Upper limit = + E = 0.3642 + 0.0150= 0.3792

The 95% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel is ( 0.3492, 0.3792)

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

Here   = x2 / n = 1222 / 3929 = 0.3110

Lower limit = - E = 0.3110 - 0.0145= 0.2965

Upper limit = + E = 0.3110 + 0.0145 = 0.3255

The 95​% confidence interval estimate for the population proportion of travelers who said that reputation was very important in choosing an airline is ( 0.2965,  0.3255).

orchestra answered 2 years ago
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