Chapter 8

For a 99% confidence interval, α =

.01

The confidence coefficient equal to ______.

1 - α

The confidence coefficient equals

1 - α

The sampling distribution of estimator XX 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

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

51

Alpha (α) is often referred to as the _______ of _______.

Level, Significance

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

Normal

Each t distribution is identified by its ______.

degrees of freedom

One 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 confidence level and sample size, the width of the interval is wider for a

larger standard deviation.

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

n = (zα/2E)2 pˆ (1 - pˆ)

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/2σˆ/ E)2

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

normal

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

normal

The estimator X (line above) follows a normal distribution when the underlying population follows a _______ distribution.

normal

The estimator XX follows a normal distribution when the underlying population follows a ________ distribution.

normal

In order to derive a confidence interval for μ, the estimator X (line above X) must have a

normal sampling distribution.

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

p(line above) ± zα/2 ⋅ √p(1−p)n

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

p, p(line above p)

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

population, variance

A confidence interval can be interpreted as a Multiple choice question. point estimate used to estimate an unknown parameter. range of values used to estimate an unknown population parameter. margin of error.

range of values used to estimate an unknown population parameter.

If the minimum and maximum values of the population are available, a rough approximation for the population standard deviation is given by its _________ divided by __________.

range, 4

The ______ p (line above) 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 standard deviation, the width of the interval is wider for a Multiple choice question.

smaller sample size.

The probability of error α for a 99% confidence interval is

.01

For a 95% confidence interval, α =

.05

For a 95% confidence interval, α =_________.

.05

The required sample size for estimating a population proportion is largest when pˆequals __________ .

.5

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

normal

The sampling distribution of estimator XX 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

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

.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.

Which of the following is the correct formula for the margin of error in the interval estimation of p?

zα/2 ⋅ √p(1−p)n

Which of the following is the correct formula for the margin of error in the interval estimation of p? Multiple choice question.

zα/2 ⋅ √p(1−p)n

The Greek letter ______ denotes the level of significance.

a

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

selecting a larger sample size.

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√

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 μ?

zα/2 σˆ E

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

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

E zα/2 pˆ

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

np ≥ 5 and n(1 - p) ≥ 5

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.

How does an interval estimator differ from a point estimator?

An interval estimator provides a range of values for the population parameter whereas a point estimator provides a single value.

True or false: the tdf distribution is bell-shaped and symmetric around 0.

T

True or false: For a given sample size n and population standard deviation σ, the lower the confidence level 100(1-α)%, the narrower the confidence interval

True

How do the tdftdf and z distributions differ?

The tdf distribution has broader tails (it is flatter around zero).

The population proportion p is the essential descriptive measure for a ___________ variable.

categorical

Larger sample sizes _______ more.

cost

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

wider