business statistics and analytics in practice 9th edition

For a 99% confidence interval, α =

.01

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

20

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

Point estimate ± margin of error

A confidence interval can be interpreted as a

range of values used to estimate an unknown population parameter.

If a 95% tolerance interval for the actual weight of sacks of sugar sold as containing 10 pounds is [9.90, 10.10] then

we estimate that 95% of all sacks will contain between 9.90 and 10.10 pounds of sugar.

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

population parameter

The ________ p̂p̂ is used as the point estimator of the ________ p.

sample proportion, population proportion

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

.95

The value of t.50 is

0

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

Widens

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.

Each t distribution is identified by its

Degree of freedom

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

The following table lists tdf values for selected upper-tail probabilities and degrees of freedom df. If df=5 and α=0.05, find tα/2,df.

2.571

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

desired level of confidence.

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 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 standard error is equivalent to

s/n

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.

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 mean length of life of AAA batteries. You have the following data: xx=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

.2

The value of t.025when the degrees of freedom are 12 is 2.179. The area to the left of -2.179 is

0.025

What is the confidence level if α = 0.10

90%

What is the confidence level if α = 0.05

95%

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

How do the t and z distributions differ

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

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

The point estimator for the population proportion is

p̂

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.

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

.05

The probability of error α for a 90% confidence interval is ____ and the probability of error α for a 99% confidence interval is ____.

.10, .01

Suppose you choose a sample of size 16 from a normal population and find xx =1.55 and s =0.44. The standard error of xx equals

.11

If a 95% confidence interval for μ based on n = 50 has margin of error = 1, what would the margin or error become if you took 200 observations

.5

If α equals 0.05, then the confidence level equals

.95

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

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

The confidence level equals

1-a

The following table lists tdf values for selected upper-tail probabilities and degrees of freedom df. If df=6 and α=0.05, find tα,df.

1.943

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

The confidence level is equal to

100 x (1 - α)%.

Suppose that in a preliminary sample of size n = 20, you find s = 12.85. How large a sample should you choose if you wish to construct a 95% confidence interval for μ having margin of error 2.5

118

The following table lists tdf values for selected upper-tail probabilities and degrees of freedom df. If df=6 and α=0.05, find tα/2,df.

2.447

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

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 xx = 35. Recall that z0.025=1.96. A 95% confidence interval for the population mean is equal to

35±1.96100√25

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

60

Suppose the standard error of xx is 0.10 and s = 0.30. The sample size must be

9

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%

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.

All of the following are characteristics of the z and t distributions EXCEPT

Bimodal

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

If we want a 90% confidence interval for a population total τ, we multiply the endpoints of a 90% confidence interval for μ by

N

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

Regardless of the sample size, the estimator xx follows a normal distribution when the underlying population follows a distribution.

Normal

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

Suppose we use the same data set to construct a 95% tolerance interval and a 95% confidence interval. Consider the relative lengths of the intervals.

The confidence interval will be shorter.

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

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

Suppose you are interested in designing a medical device that will fit comfortably on the wrists of 99% of all adult patients. To do this, should you be interested in a 99% tolerance interval for wrist sizes or a 99% confidence interval for the mean wrist size

Tolerance interval

The t distribution is bell-shaped and symmetric around 0

True

If the population standard deviation is unknown and we wish to calculate the sample size required to ensure our confidence interval has margin of error E, we must

choose a preliminary sample; estimate σ by s; and use a t value rather than a z value

The standard error of xx is NOT affected by the

confidence level

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, xx must be based on a sample which

has size n≥30

A t distribution

has slightly broader tails than the z distribution

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 xx follows a normal distribution when the sample size is large enough. As a rule-of-thumb, we use the following

n ≥30.

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

The parameter p represents the

population proportion.

When the population standard deviation is unknown, the standard error for the sample mean is calculated as

s/√nn.

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

selecting a larger sample size

As the degrees of freedom increase, the t distribution becomes more ______ a standard normal distribution

similar to

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 process of choosing a preliminary sample; estimating σ by s; and using a t value rather than a z value is used to calculate a required sample size when

the true population standard deviation is unknown

Given that we are sampling from a normal population, a 100(1 - α)% confidence interval for the population mean when the population standard deviation is not known is calculated as

xx± tα/2,dfs√nsn.