SB 9.1, 9.3, 9.4

For a 99% confidence interval, α =

0.01

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

0.05

Suppose you are constructing a confidence interval for the mean length of life of AAA batteries. You have the following data: x(bar)=250, n=25, σ=0.5, and zα/2=z0.025=1.96. The margin of error for a 95% confidence interval is closest to:

0.2

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

0.95

If α equals 0.05, then the confidence level equals

0.95.

The confidence level equals

1 - α.

The confidence level is equal to

100 x (1 - α)%.

A 95% confidence interval for the population mean is calculated as [40, 80]. The margin of error for this interval is _______

20

A sample of size 25 is drawn from a normal population with a population standard deviation of 100. Suppose the mean of the sample is x(bar) = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to

35±1.96 100/√25.

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

margin of error.

The sampling distribution of estimator x(bar) follows a normal distribution when the sample size is large enough. As a rule-of-thumb, we use the following:

n ≥30.

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

normal

Regardless of the sample size, the estimator x(bar) follows a normal distribution when the underlying population follows a ______ distribution

normal

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

normal distribution.

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

np ≥ 5 and n(1 - p) ≥ 5.

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

p, p̂

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

population variance is unknown.

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

p̂ ± z α/2 √(p̂(1-p̂)/n)

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.

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(bar)−μ) / (s/√n)

Suppose we wish to derive a confidence interval for the mean of a left-skewed population. In order to derive a valid confidence interval for μ, we must rely on ___________

the Central Limit Theorem

Suppose you have a random sample from a population whose standard deviation σ is known. If you construct both a 90% and a 95% confidence interval for μ, which interval will be shorter?

90%

What is the confidence level if α = 0.05?

95%

A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then

95% of the confidence intervals computed will contain the population mean.

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

zα/2 √ ((p̂(1-p̂))/n)

For a 95% confidence interval, α =

0.05

A 95% confidence interval for the population proportion is calculated as [0.40, 1.00]. The margin of error for this interval is _______.

0.30

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

Suppose you wish to construct a 95% confidence interval for μ having margin of error 1 and you know σ = 3.2. How large would your sample size need to be?

40

If samples of size n are drawn repeatedly from a given population and each sample is used to construct a 95% confidence interval for μ

5% of the confidence intervals will fail to contain μ.

A sample of size 25 is drawn from a normal population. Suppose the sample mean x(bar) = 50 and that the margin of error for a 95% confidence interval is 10. A 95% confidence interval for the mean is

50±10.

Suppose you wish to construct a 99% confidence interval for μ having margin of error 2 and you know σ = 5.8. How large would your sample size need to be?

56

A 95% confidence interval for the population mean is constructed as 6±2. What is the point estimate of μ?

6

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

higher confidence level.

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.

The two main components of a confidence interval are the

point estimate and the margin of error.

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

selecting a larger sample size.

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

x(bar) ± z (α/2) (σ√n).

The sample size formula for estimating a proportion using a confidence interval with margin of error E involves the product p(1-p). This product is not known. A conservative approach is to use

p(1-p) = 0.25.

A 99% confidence interval is a range of values that should include a _______ with 99% confidence.

population parameter

If we use the same data set to compute both 95% and 99% confidence intervals for μ, the margin of error for the 95% confidence interval would be _____ the margin of error for the 99% confidence interval.

less than

A confidence interval narrows if the following is accomplished:

the sample size increases. the chosen confidence level decreases.

True or False: A confidence interval is constructed around the population mean and makes inference about the sample mean.

False

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 a valid form of a confidence interval?

Point estimate ± margin of error

How is a confidence interval for the mean different from a point estimate of the mean?

The point estimate is the single number x(bar) while a confidence interval is an entire interval of values which is intended to contain μ.

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

True or false: To reduce the margin of error for a confidence interval, take a larger sample size.

True

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.