A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.7. E Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about p if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 51. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error increases. O B. The margin of error decreases. O C. The margin of error does not change. (c) Construct a 99% confidence interval about p if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.)Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? O A. As the level of confidence decreases, the size of the interval decreases. O B. As the level of confidence decreases, the size of the interval increases. O C. As the level of confidence decreases, the size of the interval stays the same. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? O A. No, the population does not need to be normally distributed. O B. Yes, the population does not need to be normally distributed. O C. Yes, the population needs to be normally distributed. O D. No, the population needs to be normally distributed