Recall: p= = ; The sampling distribution of p is approximately normal with mean p and standard deviation / p(1- p) provided ap and a(1 - p) are > 5. The test statistic for p is given by: = =- p-P Vp(1- p) The confidence interval estimator for p is given by: ptz V(1- p) 4 (a) In a random sample of 200 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes. (b) Repeat part (a) with n = 500. (c) Repeat part (a) with n = 1000. (d) Describe the effect on the confidence interval estimate of increasing the sample size. [20 marks]