Question

7. In a survey of 4000 travelers, 1500 said that location was very important for choosing a hotel and 1200 said that reputation was very important in choosing an airline. 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).

Answer 1

a)

sample proportion, = 0.375
sample size, n = 4000
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.375 * (1 - 0.375)/4000) = 0.0077

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0077
ME = 0.0151

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.375 - 1.96 * 0.0077 , 0.375 + 1.96 * 0.0077)
CI = (0.36 , 0.39)

b)

sample proportion, = 0.3
sample size, n = 4000
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.3 * (1 - 0.3)/4000) = 0.0072

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0072
ME = 0.0141

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.3 - 1.96 * 0.0072 , 0.3 + 1.96 * 0.0072)
CI = (0.286 , 0.314)

c)

we are 95% confident that the proportion of travelers who said that location was very important for choosing a hotel. is between 0.36 and 0.39

we are 95% confident that the population proportion of travelers who said that reputation was very important in choosing an airline. is between 0.286 and 0.314