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What is the most typical form of a calculated confidence interval?

Point estimate ± margin of error

The confidence coefficient equals

1 - α

The sampling distribution of estimator X follows a normal distribution when the underlying population is normally distributed and/or when the sample size is large enough. As a "rule of thumb" we use a sample size of at least

30

If the underlying population is not normally distributed, then by the central limit theorem, the sampling distribution of X will be approximately normally distributed if n>

30 or thirty

When calculating the required sample size for a mean CI, if n=50.13, the sample size we use is

51

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

n = (zα/2σ̂E)zα/2σ̂E2

In order to construct a confidence interval for μ, the sampling distribution of the estimator X must follow or approximately follow a(n) distribution

normal

In order to derive a confidence interval for μ, the estimator X must have a

normal sampling distribution.

You use sample statistics to make inferences about the unknown population

parameters

Statisticians like in their interval estimates.

precision

A confidence interval can be interpreted as a

range of values used to estimate an unknown population parameter

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

margin of error

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

selecting a larger sample size.

Precision in interval estimates is implied by a(n) margin or error.

small

is a subset of the population

sample

When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given standard deviation are

the confidence level and the sample size.

Alpha (α) is often referred to as the level

significance

When rounding a noninteger sample size, you always round

up

Match these terms from a mean confidence interval formula with their meaning.

xx Sample mean. Zα/2Zα/2 Value from the standard normal table. n Sample size. σ Standard deviation. σnσn Standard error.

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

x−μS/n√

As df increases, the tdf distribution becomes similar to the distribution

z

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

zα/2 E p̂

For the 90% confidence interval, the confidence coefficient equals and α equals

0.90 0.10

A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?

0.95

Which of the following characteristics describe both the z and tdftdf distributions?

asymptotic tails bell-shaped symmetric around 0

The allowed probability that an interval estimate of a population mean will not contain μ is referred to as the

level of significance.

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

normal

The formula for a mean confidence interval is valid only if X (approximately) follows a distribution

normal

consists of all items of interest in a statistical problem.

population

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

population variance

Each t distribution is identified by its ______.

degrees of freedom

Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the confidence interval is ______ for a greater confidence level.

wider

True or false: A confidence interval provides a range of values that should contain a population parameter with a certain level of confidence.

True

True or false: the tdftdf distribution has slightly broader tails than the z distribution.

True

In order to construct a confidence interval for the population mean μ or the population proportion p, it is essential that the sampling distributions of X and P follow, or approximately follow, a

normal

The confidence level is equal to ______.

100 x (1 - α)%

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.

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

smaller sample size.

Which of the following are components of the formula for selecting n to estimate μ?

σ̂ E zα/2

Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of X and the

desired level of confidence.

When calculating the required sample size for a proportion CI, if you do not have an estimate of the proportion, you should use a value of

.5

A particular value of the estimator is called an

estimate

A t distribution

has slightly broader tails than the Z distribution.

A 95% confidence interval for the population mean implies that

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

A confidence interval is also referred to as an

interval estimate

For a given confidence level and sample size, the larger the population standard deviation, the the confidence interval.

larger

A 95% confidence interval for the population mean is constructed as 6 ± 2. The probability of error, α is

0.05

For a 95% confidence interval, α =

0.05