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