Learn Smart Chapter 8

A confidence interval narrows if..

1. the sample size increases 2. the chosen confidence level decreases

A 95% confidence interval for the population proportion is calculated as (0.40, 1.00) The margin of error for this interval is.

First find the point estimate (0.40 + 1.00)/2 = 0.70 Then margin of error can be found as 1.00-0.70=0.30 or 0.70-0.40=0.30

Which of the following is a descriptive measure for a qualitative variable?

Proportion

a t distribution

has slightly broader tails than the z distribution

higher confidence level

increases the margin of error. Increasing the margin of error leads to a wider interval

When the population standard deviation is unknown, the standard error for the sample mean is calculated as

s/√n

When the confidence level increases from 95% to 99%, the confidence interval for the population mean____.

widens

All of the following are components of the formula for selecting n to estimate µ.

σ^, E(desired margin of error), z (alpha/2)

If α equals 0.01, then the confidence coefficient equals

0.99

The parameter ____ represents the proportion of successes in a population and the statistic ______ represents the proportion successes in a sample

p, p^-(p bar)

All of the following are components of the formula for selecting n to estimate p

p^, desired margin of error, z (alpha/2)

in order to derive a confidence interval for µ,the estimator Xbar must have a

normal sampling distribution

Confidence level

The standard error of the sample mean is NOT affected by the

When the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the

normal distribution

If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic ______ follows the t distribution with n-1 degrees of freedom

T = xbar - µ/ s/√n

All of the following are characteristics of the Z and t (df) distributions?

asymptotic tails symmetric around 0 bell-shaped

When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?

confidence interval for the population proportion