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

a) True

b) True

c) True

d) False

e) False

Step-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 formula

ME= where

As 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 mean

True.

(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 population

False. 90% confidence interval for a population mean is wider than an 95% confidence interval for the same population

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