Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of

1,000

passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the

1,000

passengers,

363

had more than one bag. Complete parts a through d below.

a. Based on this sample, develop and interpret a
95%
confidence interval estimate for the proportion of the traveling population that would have been impacted had the one-bag limit been in effect.

Determine the confidence interval.

??

———
??

(Round to three decimal places as needed. Use ascending order.)

Which statement below correctly interprets the confidence interval?

A.

There is a
0.95
probability that the sample proportion of passengers with more than one carry-on bag is in the interval.

B.

There is
95%
confidence that the population proportion of passengers with more than one carry-on bag is in the interval.

C.

Of all the possible population proportions of passengers with more than one carry-on bag,
95%
are in the interval.

D.

There is a
0.95
probability that the population proportion of passengers with more than one carry-on bag is in the interval.

b. A certain plane has a capacity for
519
passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.

An interval estimate is from
??
to
??
passengers.

(Round to the nearest whole number as needed.)

c. Suppose the airline also noted whether the passenger was male or female. Out of the
1,000
passengers observed,
615
were
female.
Of this group,
281
had more than one bag. Using these data, obtain and interpret a
95%
confidence interval estimate for the proportion of
female
passengers in the population who would have been affected by the one-bag limit.

Determine the confidence interval.

??

———
??

(Round to three decimal places as needed. Use ascending order.)

Which statement below correctly interprets the confidence interval?

A.

Of all the possible population proportions of
female
passengers with more than one carry-on bag,
95%
are in the interval.

B.

There is a
0.95
probability that the population proportion of
female
passengers with more than one carry-on bag is in the interval.

C.

There is
95%
confidence that the population proportion of
female
passengers with more than one carry-on bag is in the interval.

D.

There is a
0.95
probability that the sample proportion of
female
passengers with more than one carry-on bag is in the interval.

d. Suppose the airline decides to conduct a survey of its customers to determine their opinion of the proposed one-bag limit. The plan calls for a random sample of customers on different flights to be given a short written survey to complete during the flight. One key question on the survey will be: "Do you approve of limiting the number of carry-on bags to a maximum of one bag?" Airline managers expect that only about
20%
will say "yes." Based on this assumption, what size sample should the airline take if it wants to develop a
95%
confidence interval estimate for the population proportion who will say "yes" with a margin of error of
±0.02?

The airline should survey
?
passengers.

(Round up to the nearest whole number as needed.)

Name: Most major airlines allow passengers to carry two pieces of luggage (
Uploaded: 2024-03-20T07:07:00.000Z
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Description: Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One re

Question

Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of

1,000

passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the

1,000

passengers,

363

had more than one bag. Complete parts a through d below.

a. Based on this sample, develop and interpret a

95%

confidence interval estimate for the proportion of the traveling population that would have been impacted had the one-bag limit been in effect.

Determine the confidence interval.

??

———

??

(Round to three decimal places as needed. Use ascending order.)

Which statement below correctly interprets the confidence interval?

A.

There is a

0.95

probability that the sample proportion of passengers with more than one carry-on bag is in the interval.

B.

There is

95%

confidence that the population proportion of passengers with more than one carry-on bag is in the interval.

C.

Of all the possible population proportions of passengers with more than one carry-on bag,

95%

are in the interval.

D.

There is a

0.95

probability that the population proportion of passengers with more than one carry-on bag is in the interval.

b. A certain plane has a capacity for

519

passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.

An interval estimate is from

??

to

??

passengers.

(Round to the nearest whole number as needed.)

c. Suppose the airline also noted whether the passenger was male or female. Out of the

1,000

passengers observed,

615

were

female.

Of this group,

281

had more than one bag. Using these data, obtain and interpret a

95%

confidence interval estimate for the proportion of

female

passengers in the population who would have been affected by the one-bag limit.

Determine the confidence interval.

??

———

??

(Round to three decimal places as needed. Use ascending order.)

Which statement below correctly interprets the confidence interval?

A.

Of all the possible population proportions of

female

passengers with more than one carry-on bag,

95%

are in the interval.

B.

There is a

0.95

probability that the population proportion of

female

passengers with more than one carry-on bag is in the interval.

C.

There is

95%

confidence that the population proportion of

female

passengers with more than one carry-on bag is in the interval.

D.

There is a

0.95

probability that the sample proportion of

female

passengers with more than one carry-on bag is in the interval.

d. Suppose the airline decides to conduct a survey of its customers to determine their opinion of the proposed one-bag limit. The plan calls for a random sample of customers on different flights to be given a short written survey to complete during the flight. One key question on the survey will be: "Do you approve of limiting the number of carry-on bags to a maximum of one bag?" Airline managers expect that only about

20%

will say "yes." Based on this assumption, what size sample should the airline take if it wants to develop a

95%

confidence interval estimate for the population proportion who will say "yes" with a margin of error of

±0.02?

The airline should survey

?

passengers.

(Round up to the nearest whole number as needed.)

Accepted Answer

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