stats chapter 8

a sample of 16 is drawn for a normal population with an unknown population SD. The sample mean and the sample SD are calculated as 50 and 25, respectively. For a 95% confidence interval z0.025 and t0.025,15= 2.131. A 95% confidence interval for the population mean is equal to

...

a 95% confidence interval for the population mean is constructed as 6 +- 2. What is the probability of error, a?

0.05

suppose you are constructing a confidence interval for the mean length of life of AAA batteries. You have the following data: x- =250, n=25, ó=0.5, and za/2=z0.025=1.96. The margin of error for a 95% confidence level is closest to

0.2

a 95% confidence interval for the population proportion is calculated as. The margin of error for this interval is

0.30

assume p- =0.40 in a sample size of n=100. in addition, z0.025=1.96 and t0.025,99=1.984. A 95% confidence interval for the population proportion is

0.40 +- 1.96 *sqrt(0.40(1-0.40)/100)

the required sample size for estimating a population proportion is largest when p^ equals

0.50

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

table lists t df values for selected upper-tail probabilities and degrees of freedom. If df=6 and a=0.05, find t a,df

1.943

a 95% confidence interval for the population mean is calculated as. The margin of error for this interval is

20

for a 95% confidence interval for the population mean, if sample of size n are drawn repeatedly from a given population, then

5% of the sample means will fall outside of the corresponding confidence interval

a sample of 25 is drawn from a normal population. A sample mean of 50 is calculated. For a 95% confidence interval, the margin of error is 10. A 95% confidence interval for the mean is

50 +- 10

each t distribution is identified by its

degrees of freedom

a 95% confidence interval for the population mean implies that

for repeated sample, 95% of the sample means will fall within the interval

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

increase the sample size

suppose you are constructing a confidence interval for the population mean. For a given sample size and population SD, 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

Alpha (a) is often referred to as the

level of significance

for a desired margin of error E, the minimum sample size required to estimate a 100(1-a)% confidence interval for the population mean is

n = ((za/2 ó^) / E)^2

for a desired margin of error D, the minimum sample size required to estimate a 100(1-a)% confidence interval for the population proportion is

n = (z a/2) / D)2^p(1-^p)

when constructing a confidence interval for the population mean when the population SD is unknown, the degrees of freedom for the t-distribution are defined as

n-1

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

normal distribution

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

normal sampling distribution

the sampling distribution of the sample proportion can be approximated by a normal distribution when

np >= 5 and n(1-p) >= 5

a 100(1-a)% confidence interval for the population proportion is

p' +- z a/2 *sq rt p'(1-p')/n

the parameter ___ represents the proportion of successes in a population and the statistic ___ represents the proportion successes in a sample

p, p-

all of the following are components of the formula for selecting n to estimate u except

p^

the parameter p represents the

population proportion

when estimating the population mean, the tdf distribution is used when the

population variance is unknown

a confidence interval can be interpreted as a

range of values used to estimate an unknown population parameter

when the population SD is unknown, the standard error for the sample mean is calculated as

s / sqrt n

the ___ P- is used as the point estimator for the ___ p

sample proportion, population proportion

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

smaller sample size

when constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given SD are

the confidence level and the sample size

for a 99% confidence interval, a =

0.01

a 95% confidence interval for the population mean is calculated as. The point estimate for this interval is

0.60

the point estimator for the population proportion is

p-

T/F: a confidence interval provides a range of values that should contain a population parameter with a certain level of confidence

true

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 selected n to estimate p except

o^

the mean and SD are often used to describe ___ data while the proportion is a descriptive measure that can also be used for ___ data

quantitative, qualitative

a sample of 25 is drawn for a normal population with an unknown population SD. The sample mean and the sample SD are calculated as 35 and 100, respectively. For a 95% confidence interval z0.025 and t0.025,24 = 2.064. A 95% confidence interval for the population mean is equal to

35 +- 2.064(100/sq rt5)

if a equals 0.01, then the confidence coefficient equals

0.99

the confidence level is equal to

100 x (1-a) %

the confidence coefficient equals

1-a

a sample of 25 is drawn from a normal population with a population SD of 100. A sample mean of 35 is calculated. For a 95% confidence interval z0.025 = 1.96. A 95% confidence interval for the population mean is equal to

35 +- 1.96 (100/ sqrt25)

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

margin of error

which of the following is a descriptive measure for a qualitative measure

proportion

whenever we construct a confidence interval for the population mean, the margin or error includes the standard error of x- and the

desired level of confidence

precision in interval estimates is implied by a(n) ____ margin of error

low

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/sqrtn)

a confidence interval narrows if the following is accomplished

The sample size increases The chosen confidence level decreases

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

True

sample mean is not affected by the

confidence level

a random sample of 80 observations results in 50 successes. What is the point estimate of the population proportion of successes

0.625

a random sample of 60 observations results in 42 successes. What is the point estimate of the population proportion of successes

0.7

a t distribution

has slightly broader tails than the z distribution

in order to construct a confidence interval for u, the sampling distribution of the estimator x- must follow a ____ distribution

normal

the sampling distribution of the estimator x- follows a normal distribution when the underlying population follows a _____ distribution

normal

the width of the confidence level is ___ for a greater confidence level

wider

table lists t df values for selected upper-tail probabilities and degrees of freedom. If df=6 and a=0.05, find t a/2,df

2.447