Question

(05.01 LC)

A polling company has decided to increase the size of its random sample of voters from about 2,000 people to about 4,500 people right before an election. A poll was designed to estimate the proportion of voters who favor a new law to set an 11 p.m. curfew for teenagers. What is the effect of this increase? (4 points)

a	To reduce the bias of the estimate
b	To increase the bias of the estimate
c	To reduce the variability of the estimate
d	To increase the variability of the estimate
e	This increase will have no effect because the population size is the same.

(05.05 LC)

A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90% confidence interval for the population mean or a 95% confidence interval for the population mean. How will these intervals differ? (4 points)

a	The 90% confidence interval will not be as wide as the 95% confidence interval.
b	The 90% confidence interval will be wider than the 95% confidence interval.
c	The wider interval is dependent on a larger sample size.
d	The wider interval is dependent on whether the sample is unbiased.
e	The wider interval is dependent on whether a z statistic or a t statistic is used.

Answer 1

1). the effect of this increase is:-

To reduce the bias of the estimate (a)

[ interpretation:-

because we know that ,

as sample size increases, the sampling error tends to decrease...which makes the sample size less variable ...causing in reduction of bias of the estimate]

5). these intervals will differ by:-

The 90% confidence interval will not be as wide as the 95% confidence interval(a)

[ interpretation:-

we know that, keeping sample size fixed, as the confidence level increases, our confidence interval becomes wider..in order to be more confident .

so, the 95% confidence interval will be more wider than the 90% confidence interval ]

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