Practice Problems 5
1.
In a random sample of 100
Hawk & Hummingbird Airline
(
HHA
) direct flights
from New York to Boston, the average number of passengers was 56.3, with
sample standard deviation 11.33.
a)
Construct a 95% confidence interval for the overall average number of passengers
on this route.
b)
To make a reasonable profit,
HHA
must average at least 58 passengers per flight
on this route.
The president of the airline is concerned that the average number of
passengers is less than 58.
Perform the appropriate test at
α
= 0.05.
c)
Suppose the actual overall average number of passengers on this flight is 57.
Then in part (b) a ( Type I Error, Type II Error, correct decision ) was made.
d)
Find the pvalue of the test in part (b).
e)
Using the Pvalue obtained in part (d), state your decision
( Accept
H
0
or
Reject
H
0
)
for
α
= 0.10.
f)
Describe in the context of the problem what happens if Type I Error occurs.
g)
Describe in the context of the problem what happens if Type II Error occurs.
2.
Hawk & Hummingbird Airline
wants to determine the proportion of passengers that
bring only carryon luggage to the flight from New York to Boston.
a)
In a random sample of 200 passengers, 44 passengers had only carryon luggage.
Is there enough evidence to conclude that more than 20% of all passengers have
only carryon luggage?
Use
α
= 0.10.
b)
Find the pvalue of the test in part (a).
c)
Find a 90% confidence interval for the overall proportion of passengers who have
only carryon luggage.
d)
Find the minimum sample size required in order to estimate the proportion of
passengers who have only carryon luggage to within 2% with 90% confidence,
if it is known that this proportion is at most 0.30.
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3.
In a random sample of 25 direct flights from New York to Boston by
Hawk &
Hummingbird Airline
, the sample mean flight time was 56 minutes and the sample
standard deviation was 8 minutes.
(Assume the flight times are approximately
normally distributed.)
a)
Construct a 98% confidence interval for the overall mean flight time on this route.
b)
Test whether the actual overall mean flight time on this route is 1 hour (60
minutes) or it is different at 5% significance level.
c)
Find the Pvalue of the test in part (b).
d)
Using the Pvalue obtained in part (c), state your decision
( Accept
H
0
or
Reject
H
0
)
for
α
= 0.01.
e)
Suppose that the actual overall mean flight time on this route is 58 minutes.
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 Spring '08
 Kim
 Statistics, Probability, Standard Deviation, Hummingbird Airline

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