Game Theory

1654 Words Aug 17th, 2013 7 Pages
PS II 2013 Problem Set II
1. Reading newspapers: A survey on student behavior in some major B-schools in India asked a randomly selected group of 240 students on the number of hours a week he/she reads a newspaper. The sample mean was 4.1 and standard deviation 3. We can assume that the underlying distribution (of number of hrs reading newspaper) is approximately normal.
a) What will be a 99% confidence interval of the population mean (number of hours a B-school student read newspapers/week)?
b) Suppose you perform a similar survey at IIMA with 24 randomly selected students; the sample mean and the sample standard deviation were 4.5 and 2.8 respectively. What will be a 99% confidence interval of the population mean
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Similarly, the number of defectives among the ten televisions of brand B is 2M. In order to test the null hypothesis H0: M = 2 against the alternative Ha: M > 2, the following procedure is adopted:
(i) From the six televisions of brand A, draw a random sample of size two without replacement.
(ii) From the ten televisions of brand B, draw a random sample of size two without replacement.
(iii) Reject if and only if both the televisions in at least one of the two samples are defectives.
a) What is the probability of type I error for the above test procedure?
b) Find the probability of type II error for this procedure when M equals 3.
5. Anorexia in teenage girls: Anorexia is an eating disorder that can cause a person to be dangerously underweight. A recent study analysed the effect of cognitive behavioural therapy in aiding weight gain on 29 teenage girls affected with Anorexia. Each girl’s weight was measured before and after the therapy and the weight change (positive: weight gain; negative: weight loss) was noted. The weight changes for the 29 girls had a sample mean of = 3 kilos and a standard deviation of s = 7.32 kilos. Let µ be the population mean weight change. It can be assumed that weight change follow a normal distribution in the population.
a) What would be a reasonable set of hypotheses (null and alternative) for this problem?
b) How many standard errors separate the sample average weight change of the 29 girls and the null value

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