1. A sample poll of 400 voters chosen at random from all voters in a given district in Manila indicated that 58% of them were in favor of a particular candidate. Find a) 95%, b) 99% confidence limits for the proportion of all voters in favor of this candidate. 2. In 50 tosses of a coin, 30 heads were obtained. Find a) 95%, b) 99% confidence limits for the proportion of heads which would be obtained in an unlimited number of tosses of the coin. 3. Independent random samples were selected from populations 1 and 2. The sample sizes, means and variances are as follows: population 1 2 Sample size 200 200 Sample mean 2.44 3.11 Sample variance 1.44 2.64 Find a a) 95%, b) 99% confidence interval for estimating the difference in the population means ( 1 - #, ). 1. In a survey conducted by the a university research center, students spend more than 8 hours surfing the internet . Suppose that of the 280 male and female students tested, Ow = 95 played internet games and o = 105 were busy with research in the internet. The following results were observed: population Games Research Sample size 100 140 Percent 959% 75% Construct a a) 95%, b) 99% confidence intervals for the difference in the two population proportions