ch 8 reading questions

The confidence coefficient equals

1 - α

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

2

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

Point estimate ± margin of error

A 95% confidence interval for the population mean implies that

for repeated samples, 95% of the intervals will contain the population mean.

The parameter p represents the ______.

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

smaller sample size.

The equation for a confidence interval for μ when the value of σ is unknown is

x ± tα/2,df ⋅ s/√n

What is the value of zα/2 for a 90% confidence interval for the population mean?

1.645

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

95% of the intervals will contain the population mean.

How does an interval estimate differ from a point estimate?

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

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

Za/2 √p(1-p)/n

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

normal sampling distribution.

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

small

The equation for a confidence interval for μ when the value of σ is known is

x̄±z α/2 ⋅ σ/√n

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 )

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 the following to check sample size:

n ≥ 30

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

np ≥ 5 and n(1 - p) ≥ 5

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

population standard deviation is unknown.

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.

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

How do the tdf and z distributions differ?

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

Which of the following happens when the sample size gets smaller for the unknown σ case? Select all that apply.

The confidence interval gets wider. The t-value gets larger.

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

0.95

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.

As α becomes smaller, what happens to the value of tα,df for a given df = n - 1?

It stays the same. It gets closer to 0.

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−μ / S/√n

The shape of each t distribution depends upon its ______.

degrees of freedom

Which of the following are components of the formula for selecting n? Select all that apply.

desired margin of error zα/2 pˆ

A t distribution

has slightly broader tails than the Z distribution.

Alpha (α), the probability the interval does not contain the population mean, is often referred to as the

level of significance.

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

margin of error.

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/2σˆE) ^2

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

normal

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

p(line over it) ± zα/2 ⋅ √p(1−p)/n

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

p, p(line over it)

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

quantitative, qualitative

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

selecting a larger sample size.

A confidence interval narrows if the following is accomplished:

the chosen confidence level decreases. the sample size increases.

When the confidence level increases from 95% to 99%, the confidence interval for the population mean ________.

widens

The required sample size for estimating a population proportion is largest when pˆ 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. Then the margin of error is

1 hour.

Which of the following is a descriptive measure for a qualitative variable?

Proportion

An estimate of the population standard deviation is necessary to determine how large of a sample size is needed to estimate the population mean. How can the population standard deviation be estimated?

Range/4

As the population standard deviation decreases and everything else remains constant, the width of the confidence interval _____.

decreases

One way to reduce the margin of error is to

increase the sample size.

When constructing a confidence interval for the population mean when the population standard deviation is unknown, the degrees of freedom for the t distribution are defined as ______.

n - 1

The point estimator for the population proportion is ______.

p(line over it)

All of the following are components of the formula for selecting n to estimate μ EXCEPT:

pˆ

A confidence interval can be interpreted as a

range of values used to estimate an unknown population parameter.

A proportion must be between

0 and 1.

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.

The Greek letter ______ denotes the level of significance.

α

What is the value of zα/2 for a 99% confidence interval for the population mean?

2.576

A certain type of light bulb is advertised to have a life of about 100 hours of use. With a certain level of confidence, it is advertised that the life is between 90 and 110 hours. If 100 hours is the point estimate, then the margin of error is

10 hours.

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 characteristics describe both the z and tdf distributions? Select all that apply.

asymptotic tails bell-shaped symmetric around 0

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

True

True or false: X follows a normal distribution in estimating the population mean.

True