5. True or False. (a) All other factors remaining the same, increasing the sample size, n, will decrease the width of a con dence interval. (b) We expect 95% of all 95% con dence intervals for the population mean to contain the sample mean. (c) The t-distribution is symmetric and centered at the population mean . (d) The t-distribution is very similar to the standard normal distribution regardless of its degrees of freedom. (e) All other factors remaining the same, a 90% con dence interval for a population mean is narrower than an 95% con dence interval for the same . 1

Answer:a) Trueb) Truec) Trued) Falsee) FalseStep-by-step explanation:(a) All other factors remaining the same, increasing the sample size, n, will decrease the width of a confidence interval.True. Confidence intervals are calculated by calculating margin of error (ME) around the mean using the formulaME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where z is the corresponding statistic (z-score or t-score) s is the standard deviation of the sample(or of the population if it is known) N is the sample sizeAs the formula suggests, all other factors remaining the same, if we increase N, ME decreases. b) We expect 95% of all 95% confidence intervals for the population mean to contain the sample mean.True. This is what 95% confidence level assumes. (c) The t-distribution is symmetric and centered at the population meanTrue.(d) The t-distribution is very similar to the standard normal distribution regardless of its degrees of freedom.False. As the degrees of freedom increases t-distribution resembles the standard normal distribution. For small sample sizes (<30), this is not true. (e) All other factors remaining the same, a 90% confidence interval for a population mean is narrower than an 95% confidence interval for the same populationFalse. 90% confidence interval for a population mean is wider than an 95% confidence interval for the same population