Chapter 8 Learn Smart

AAA batteries are advertised to have a life of about 9 hours of use. With a certain level of confidence, it is advertised that the life is between 8-10 hours. if 9 hours is the point estimate, then the margin of error is

1 hour

a 95% confidence interval for the population mean is constructed as 6+-2. What is the point estimate?

6

in order to derive a confidence interval for u, the estimator x- must have a

normal sampling distribution

The parameter p represents the ____

population proportion

the most practical way to reduce the margin of error is by

selecting a larger sample size

(T/F) A 95% confidence interval for u implies that if numerous samples are taken from a population, 95% of the intervals will contain u.

trueee

Given that we are sampling from a normal population, a 100(1-a)% confidence interval for the population mean when the population standard deviation is not known is a calculated as:

x⎯± tα/2,df s/√n

A 95% confidence interval for the population proportion is calculated as (0.40, 0.80) The point estimate for this interval is _____

.60

for a 95% confidence interval, a=

0.05

(T/F) A confidence interval provides a range of values that should contain a population parameter with a certain level of confidence.

true

A random sample of 80 observations results in 50 successes. The point estimate of the population proportion of successes is _____

0.625

The following table lists t a,df values for selected upper-tail probabilities a and degrees of freedom df. if df= 6 and a =0.05, the t a,df = _____

1.943

the confidence level is equal to ____.

100 x (1-a)%

The estimator X follows a normal distribution when the underlying population follows a _____ distribution.

Normal

when the sample size is sufficiently larger, we can approximate the sampling distribution of the sample proportion using the _____ distribution.

normal

if a equals 0.05, then the confidence coefficient equals ______.

.95

suppose you are constructing a confidence interval for the population mean. For a given sample size and population standard deviation, how will the width of the interval change as the confidence level increases?

it gets larger

suppose you are constructing a confidence interval for the population mean. for a given confidence level and sample size, the width of the interval is wider for a

larger standard deviation

a confidence interval is constructed by using the point estimate as a base, to which we add and subtract the

margin of error

when comparing two confidence intervals, the one that has the smaller margin of error has a

more precise estimate of the parameter

The mean and standard deviation are often used to describe ____ data while the proportion is a descriptive measure that can also be used for ____ date

quantitative, qualitative

the two pieces of information that are necessary to determine the value of t are....

"the level of significance" AND "the sample size or degrees of freedom"

Alpha (a) is often referred to as the

level of significance

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= x-u / (s/√n)

A t distribution

has slightly broader tails than the z distribution

a confidence interval narrows if the following is accomplished:

the chosen confidence level decreases the sample size increases

(T/F) The tdf distribution is bell-shaped and symmetric around 0.

ture