(a)In a poll of 10,000 voters selected at random from all voters in a certain district, it is found that 5,180 voters are in favor of particular candidate. Test the null hypothesis that the proportion of all the voters in the district, who favor the candidate is equal to or less than 50% against the alternative that it is greater than 50%. Use a 0.05 level of significance.

(b)The 95% confidence interval for the mean length of life of a particular brand of light bulb is (1023.3 h, 1101.7 h). This interval is based on results from a random sample of 36 light bulbs. Find the 99% confidence interval for the mean length of life of this brand of light bulbs, assuming that the length of life is normally distributed.