SB 9.1,9.3,9.4

For a 99% confidence interval, α =

0.01.

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 proportion is calculated as [0.40, 0.80]. The point estimate for p is _______.

0.60

The confidence level equals

1 - α.

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

Suppose you wish to construct a 95% confidence interval for μ having margin of error 2 and you know σ = 3.2. How large would your sample size need to be?

10

n

10

The confidence level is equal to

100 x (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 value of zα/2 for a 99% confidence interval for the population mean?

2.575

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

6

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.

p = 1/6

Long-run proportion of sixes thrown with a fair die.

Which of the following is a valid form of a confidence interval?

Point estimate ± margin of error

p̂ = 0.19

Proportion of times sixes are rolled in 100 rolls of a fair die.

p̂ = 0.52

Proportion of voters preferring a candidate in a poll of 300 voters.

p = 2/7

Proportion of weekend days per week.

Whenever we construct a confidence interval for the population mean, the margin of error is based upon the standard deviation of x(bar) and the

desired level of confidence.

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.

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

margin of error.

Suppose you are interested in estimating the proportion of business tax forms where a particular type of deduction is miscalculated. If you believe the proportion of forms with this miscalculation is no more than 35%, how would you determine the sample size required to achieve a 99% confidence interval having margin of error 0.02?

n = 0.2275[2.575/.02]^2

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 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.

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

p, p̂

The two main components of a confidence interval are the

point estimate and the margin of error.

The parameter p represents the

population proportion.

When estimating the population mean, the t 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.

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

selecting a larger sample size.

⎯⎯ x −μ s/√10

t

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

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.

A confidence interval narrows if the following is accomplished:

the sample size increases. the chosen confidence level decreases.

True or false: A 95% confidence interval for μ implies that if numerous samples are taken from a population, 95% of the intervals will contain μ.

true

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

true

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

x(bar)±zα/2*σ √n.

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

zα/2√pˆ(1−pˆ) n

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

50±10.

A 95% confidence interval for the population mean is calculated as [40, 80]. The point estimate for μ is _______.

60

If α equals 0.01, then the confidence level equals

0.99.

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.

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

np ≥ 5 and n(1 - p) ≥ 5.

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

Suppose a brokerage house wishes to construct a confidence interval for p, the proportion of its clients who are dissatisfied with its services. In a sample of 150 clients, it found a 95% confidence interval for p is [0.136, 0.264]. How large a sample should the firm choose if it wishes the interval to have margin of error 0.03?

830

df

9

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

False

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

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

⎯⎯ x −μ σ/√10

Z

A random sample of 60 observations results in 42 successes. What is the point estimate of the population proportion of successes?

0.7

Assume the sample proportion is equal to 0.70 in a sample size of 100. In addition, z0.05=1.645 and t0.05,99=1.660. A 90% confidence interval for the population proportion is

0.70±1.645* √0.70(1−0.70) 100

Assume the sample proportion is equal to 0.75 in a sample size of 90. In addition, z0.05=1.645 and t0.05,99=1.660. A 90% confidence interval for the population proportion is

0.75±1.645* √0.75(1−0.75) 90

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

0.95

A random sample of 80 observations results in 50 successes. What is the point estimate of the population proportion of successes?

0.625

Suppose you wish to construct a 95% confidence interval for p having a margin of error 0.02. If you can reasonably say that p is no more than 0.3, what sample size would be required?

2017

Suppose we wish to derive a confidence interval for the mean of a right-skewed population. In order to derive a valid confidence interval for μ, x (bar) must be based on a sample which

has size n≥30.

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.