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However, you want to design a survey to gauge the opinions tot AIM students: accordingly. You want to form a 95% confidence Interval with a margin of error of 0. 05. What will be your sample size? ) What will be your sample size for the above problem If you have no Idea of the percentage of Indian adults supporting death penalty? 3. Industry and environment: In response to a recent GAS survey on whether the Government should impose strict laws to prohibit industries trot damaging the environment, 1093 out of 1232 subjects said "yes". A) The confidence Interval for p, the population proportion who would say "yes" Is (l) (0. 0, 0. 95) (II) (0. 87, 0. 90) Oil) (0. 50, 1. 00) (iv) (0. 89, 1. 00) b) What is the 99% confidence interval for 1 ? p, the population proportion who would say "no"? (I) (0. 09, 0. 4) 0. 91) (iii) (005, 0. 15) (iv) (080, 0. 95) c) Suppose that you want to do a similar survey in your locality. Accordingly, you selects random sample tot 200 people and 160 tot them said yes". What Is the 99% confidence Interval for p (the population proportion who would 1 OFF Suppose you feel that the above interval is way too wide and would like to have a shorter and more precise interval.

What should you do to achieve that? (I) Increase the confidence level and the sample size. (ii) Decrease the confidence level but increase the sample size. (iii) Decrease the confidence level and the sample size. Iv) Increase the confidence level but decrease the sample size. (v) Cannot do anything; have to accept the above interval. 4. A dealer in electronic consumer goods received a supply of six televisions of brand A and ten televisions of brand B. Out of the six televisions of brand A, an unknown number, M, are defectives.

Similarly, the number of defectives among the ten televisions of brand B is MM. In order to test the null hypothesis HO: 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? ) 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 analyses the effect of cognitive behavioral 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 Offs = 7. 2 kilos. Let p 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?