data analytics

a) To construct a confidence interval for a mean, the z distribution is used only when the Standard Deviation is known. b) To locate an appropriate t-value in the Student's t-distribution table, which of the following is not necessary (degrees of freedom; p-value; level of confidence)? c) Assuming the same sample size and same standard deviation, a 90\% confidence interval will be (equal to, greater than, less than) a 95\% confidence interval. d) When determining the sample size required to determine an estimate for a population proportion, what value of the population proportion () should be used when it is not given or known? e) True or False: The Standard Error of the Mean and the Margin of Error are the same thing. f) As the degrees of freedom increase to infinity, the t-distribution (approaches the binomial distribution, becomes positively skewed, approaches the z-distribution)