Question

True or False? The higher the confidence level, the narrower is the confidence interval for the mean. Select an answer The most efficient point estimator for the population mean ù is the sample median . Select an answer • To reduce the width of a confidence interval, we can increase the sample size n. Select an answer • As long as the population is normal with variance o’, the statistic (n-1) S2 has a Chi-squared 02 distribution with n degrees of freedom. Select an answer v When the population standard deviation o is unknown, we use the z-value of 1.96 to construct a 95% confidence interval for the mean u. Select an answer • A confidence interval is always calculated by selecting a confidence level. Select an answer v • To decrease the width of a confidence interval, we can decrease o. Select an answer v

Answer 1

a. False, the higher the confidence level, the wider the confidence interval.

for eg, a 99% confidence level is wider than a 90 % confidence interval ((+-) 4.5 % instead of 2.5 %).

b.False, the sample mean is the most efficient point estimate for population mean.

c. True, the CI width and the sample size are inversely related. The larger the size of the sample the more truely it reflects the population and hence a smaller confidence interval.

d. False, ns^2/sigma^2 follows chi square distribution wih (n-1) degrees of freedom.

e. True, z=+-1.96 is used.

f. True, a confidence interval is always based on a confidence level.

g. True, if the variation in the data decreases, the confidence interval would be smaller.