Question 4 {25 marks} A pilot study on 30 respondents was conducted to study a new marketing strategy in a mobile application. It is found that 24 respondents were male and 20 respondents preferred the new marketing strategy. Among the responderns who preferred the new marketing strategy, S'i of them were male. {a} Find the probability that a randomly selected respondent is male and prefers the new marketing strategy. [3 marks] [b] Find the probability that a randomly selected respondent is male or prefers the new marketing strategy. [3 marks] [c] If a randomly selected respondent is female, find the probability that she prefers the new marketing strategy. [4 marks] [d] Explain whether the preference in the new marketing strategy is independent of gender. [4 marks] [e] It is required to have 90% confidence in estimating the population proportion of preferring the new marketing strategy with the sampling error not greater than ELEM. Determine the optimal sample size for a future study. [5 marks] If] Explain whether the requirement on the sampling error is guaranteed after data are collected in the study in {e}. If not, determine the sample size which ensures that the requirement will be met. [5 marks]