Download Assignment 5 34KB Jul 05 2013 10:00:51 PM

Assignment 5
Note: Always explain how you arrived at our answers! No credit is given to
answers without proper motivation.
Exercise 1
A recent study under 25 graduated International Business students showed that the
net monthly salary after graduation is on average 1750 Euro. From previous research
it is known that such salaries are normally distributed and that the corresponding
standard deviation (is 200 Euros.
1)
The 95% confidence interval for the population mean, rounded to whole euros,
is: [1672 , 1828]
2)
A sample of size 62 is needed to construct a 95% confidence interval with a
maximal width of 50 euro.
A university worker claims that the mean salary for recently graduated International
Business students is 2000 euro. To test his claim, a student proposes the following
hypotheses:
H0:  = 2000
Ha: ≠ 2000.
The student performs the test by using the previously mentioned sample of 25
students. She uses a significance level of 5%.
3)
The null hypothesis must be rejected.
Exercise 2
An investor considers asking an old acquaintance to invest for him. The old
acquaintance claims that he will achieve a return rate of at least 5%. The investor
asks 9 clients of the old acquaintance about their realized returns. It turns out that
the mean realized returns of these 9 observations is 5.6%. It is known that the
returns are normally distributed with a standard deviation = 1. To decide whether
or not he should let his old acquaintance invest, the investor tests the following
hypotheses: H0:  = 5.0, Ha:  > 5.0%, where  is the expected mean return.
4)
5)
The p-value corresponding to this test is, rounded to 4 decimals accuracy,
0.2743.
At a significance level of 5%, the nullhypothesis can not be rejected.
Exercise 3
An economist is interested in studying the incomes of consumers in a particular
state. The population standard deviation () in this state is known to be $1,000. A
random sample of 49 individuals resulted in an average income of $15,000.
6)
The width of the 90% confidence interval is $235.
7)
To get a 90% confidence interval with a width of no more than $100, a sample of size
1083 is needed.
A friend of the economist proposes to test whether the income of consumers in the
state is smaller than 16000. He formulates as hypotheses: H0:  = 16000 Ha:  <
16000.
8)
The p-value for the corresponding test statistic is 0.1587.
Exercise 4
To test whether flight controllers use drugs, they are required to undergo periodic
random drug testing. For screening a simple urine test is used. For this test, it is
known that when someone uses drugs, the probability of a (correct) positive result is
96%. On the other hand, if someone does not use drugs, the probability of obtaining
a (correct) negative result is 93%. Based on past data, it is known that the probability
of drug use for a flight controller is 0.007. A positive test result puts the controller’s
job at jeopardy.
A flight controller is randomly chosen to undergo the test.
9)
The probability for a positive test result is 0.007.
10)
If the test is positive, the probability that the controller used drugs is, rounded to two
decimals accuracy, 0.09.