The manager of a fitness center wants to promote aerobic classes.

(a) The manager randomly selected 200 Hong Kong residents and found out that 80 of them had taken part in aerobic classes. Let be the proportion of Hong Kong residents who had taken part in aerobic classes. Find the 95% confidence interval for . Interpret the result. Verity the necessary conditions.

(b) If in the sample of 200 Hong Kong residents, 90 of them had taken part in aerobics classes. Keeping the level of confidence remains unchanged, without computation, explain how would this affects the confidence interval constructed in part (a)?