BUS 223 Lecture Notes - Lecture 11: Confidence Interval
25 Jun 2018
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PROPORTIONS
1. From past experience it is known that 70% of all airplane tickets sold are
round trip tickets. A random sample of 100 passengers is taken and found
that 72% of the passengers had purchased round trip tickets. At the 0.05
level of significance, does this indicate that round trip tickets are more than
70% of tickets sold?
2. A new public telephone has been installed in an airport baggage claim area.
A quarter was lost 45 of the first 300 times it was used. Construct a 95%
confidence interval for the true proportion of times that a user will lose a
quarter.
3. Fifty-four percent of all nurses in the day shift at a hospital have type O
blood. Thirty-six nurses from the dayshift are selected at random. What is
the probability that between 51% and 58% of these nurses have type O
blood?
4. Transportation officials claim that 96% of its commuter trains arrive on
time. In a random sample of 628 arriving trains, it was found that 587 of the
trains arrived on time. Is the transportation company’s claim justified at a
5% level of significance?
5. In a sample, 9 out of 52 observations are successes. Construct the confidence
interval for the true proportion of successes in the population from which the
sample was drawn with a 1% chance of error.
6. A cable company wants to know the proportion of homes in a suburban area
still using TV antennas. In other similar areas 37% of the homes use TV
antennas. Determine the sample size if the company wants to know the true
proportion with a maximum error of 0.025 at the 90% confidence level.
7. In a recent press conference a senator claimed that 55% of the American
people supported the President’s foreign policy. To test this claim, a
newspaper selected a random sample of 1000 people and 490 of them said
that they supported the President’s foreign policy. At the 1% level of
significance, is the senator’s claim justified?
8. Dr. Rogers claims that he has developed a new ointment, which is 90%
effective in treating infection. To test this claim, a medical panel tests the new
ointment on 65 people and found that 46 of them were cured. Should we
reject the doctor’s claim at the 5% level of significance?
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Document Summary
Proportions: from past experience it is known that 70% of all airplane tickets sold are round trip tickets. A random sample of 100 passengers is taken and found that 72% of the passengers had purchased round trip tickets. At the 0. 05 level of significance, does this indicate that round trip tickets are more than. 70% of tickets sold: a new public telephone has been installed in an airport baggage claim area. A quarter was lost 45 of the first 300 times it was used. Construct a 95% confidence interval for the true proportion of times that a user will lose a quarter: fifty-four percent of all nurses in the day shift at a hospital have type o blood. Thirty-six nurses from the dayshift are selected at random. What is the probability that between 51% and 58% of these nurses have type o blood: transportation officials claim that 96% of its commuter trains arrive on time.
