Please explain why the selected 4 are correct

In constructing a confidence interval for a population mean, which of the following are true? Select four (4] true statements from the list below: [ l [ 1 - Increasing the sample size will decrease the width of the confidence interval. - A confidence interval that fails to capture the population mean will also fail to capture the sample mean. - A point estimate is a single population parameter that is used to a estimate a sample statistic. - A 99% confidence interval must capture 99% of the sample values. - For a confidence level of 99%, the left-tail area of! = 0.01. - Decreasing the confidence level will increase the width of the confidence interval. - For the same sample data, a 95% confidence interval will be wider than a 99% confidence interval. - If a particular 35% confidence interval captures the population mean, then for the same sample data, the population mean will also he captured at the 83% confidence level. - The width of the confidence interval depends on the size of the confidence level. - If the point estimate and upper limit for a confidence interval are 138 and 200 respectively, then the lower limit must be 12. - If a confidence interval does not contain the population parameter, then an error has been made in the calculation. - If a confidence interval for the population mean is constructed from a sample of size n = 30, that interval must contain the sample mean