more stat stuff

As the sample size increases, what happens to the standard deviation of X^_

It gets smaller.

True or false: The test statistic for p is valid only if ¯P approximately follows a normal distribution.

True

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

True

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

symmetric around 0 asymptotic tails bell-shaped

The standard deviation of P^_ equals

√p(1−p)/n

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large is known as the

central limit theorem.

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

decreases

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

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

If we reject the null hypothesis when it is actually false we have committed

no error

A binomial distribution can be approximated by a ______ distribution for large sample sizes.

normal

The area under the entire Tdf distribution sums to

1

In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to

A number of randomly occurring events that are part of the production process.

What is a primary requirement of a "good" sample?

It is representative of the population we are trying to describe.

Which of the following are components of a control chart? Select all that apply.

Lower control limit (LCL) Upper control limit (UCL) Centerline

True or false: A process could be veering out of control if there is a trend within the upper and lower control limits of a control chart.

True

True or false: Most statistical methods presume simple random samples.

True

The central limit theorem states that as n gets larger, the sampling distribution of the sample proportion

approaches a normal distribution.

The expected value of PP is the

proportion of successes in the population.

When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical ______.

quality control

A population consists of all items of interest in a statistical problem, whereas a ______ is a subset of the population.

sample

The probability distribution of the sample mean is commonly referred to as the _____.

sampling distribution of X^_

In ______, the population is divided up into strata and then randomly selected observations are taken proportionately from each stratum.

stratified random sampling

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 proportion would be the appropriate descriptive measure when trying to estimate the

the percentage of students living off-campus.

Cluster sampling works best

when most of the variation in a population is within groups and not between groups.

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

widens

Which of the the following signs in the null would indicate a left-tailed test?

≥

A firm uses acceptance sampling when

it produces a product and at the end of the process, inspects a portion.

A sample statistic is considered biased if

it systematically over- or under-estimates the unknown parameter being estimated.

In general, the variability between sample means is ______ the variability between observations.

less than

The confidence coefficient equals

1 - α

_________ involves dividing a population into mutually exclusive and exhaustive groups, and then selecting a random sample from these groups for analysis.

Cluster sampling

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

desired margin of error zα/2 p̂

A test of H0: μ = 10 at the α significance level can be rejected if a 100(1-α)% confidence interval for μ

does not include 10.

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

level of significance.

The purpose of statistical quality control is to

maintain high-quality goods and services.

A manufacturing production process is in control if the sample means are

randomly spread out between the control limits.

A confidence interval can be interpreted as a

range of values used to estimate an unknown population parameter.

The point estimator for the population proportion is ______.

P line over it

When H0: μ ≤ 150 and xx = 160, the p-value is defined as

P(xx ≥160).

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

Point estimate ± margin of error

Bias can occur in sampling. Bias refers to

the tendency of a sample statistic to systematically over- or under-estimate a population parameter.

When a sample statistic is used to make inferences about a population parameter, it is referred to as a/an

estimator.

If X is normally distributed with expected value μ and standard deviation σ, then X^_ is normally distributed with

expected value μ and standard deviation σ/√nn.

A 95% confidence interval for the population mean implies that

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

The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as ________.

inferential statistics

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

selecting a larger sample size.

When a sample of n observations that has the same probability of being selected from the population as any other sample of n observations is called a ______.

simple random sample

Which of the following is an example of a sample statistic?

x^_

In general, the control limits of a control chart are set at ______ standard deviations from the centerline.

3

The general rule for using the finite correction factor is that the sample constitutes at least _____ of the population.

5%

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

Order the steps of formulating the competing hypotheses:

1. Identify the relevant population parameter of interest2. Determine whether it is a one or two tailed test3. Include some form of equality sign in the null hypothesis and use the alternative hypothesis

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a left-tailed test is (are):

-z0.10

The required sample size for estimating a population proportion is largest when p̂p̂ equals ______.

.50

Which of the following statements is NOT correct concerning the p-value and critical value approaches to hypothesis testing?

Both approaches use the same decision rule concerning when to reject H0.

Which one of the following is NOT a step we use when formulating the null and alternative hypotheses?

Calculate the value of the sample statistic.

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

np ≥ 5 and n(1 - p) ≥ 5

The hypothesis denoted by H0 is the ______ hypothesis and the hypothesis denoted by HA is the ______ hypothesis.

null, alternative

For a hypothesis test concerning the population proportion p, the value of the test statistic is calculated as

z = p−p0 / p0(1−p0) ÷ n √

Which of the following is true?

α = the probability of committing a Type I error; β = the probability of committing a Type II error.

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 conclusions of a hypothesis test that are drawn from the p-value approach versus the critical value approach are

always the same.

A variation in production caused by a specific event or factor that can usually be identified and eliminated is called

assignable variation.

For a given sample size n, α can only be reduced

at the expense of increasing β.

The parameter p represents the ______.

population proportion

Sample means or sample proportions being monitored by using a control chart should lie __________ .

between the upper and lower control limits.

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes

closer to a normal distribution.

A particular value of an estimator is called a/an _______.

estimate

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.

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= ((2a/2)/E)^2(Plineover)(1-Pline over)

A confidence interval narrows if the following is accomplished:

the chosen confidence level decreases. the sample size increases.

All of the following are approaches to implementing a hypothesis test EXCEPT:

the sample test

A 100(1-α)% confidence interval can be used to test which types of hypotheses tests?

A two-tailed test at the α significance level.

Which of the the following signs in the null would indicate a two-tailed test?

=

As the population proportion deviates from p = 0.50, what happens to the sample size required in order to satisfy a normal approximation?

It gets larger.

When a voter provides incorrect answers to a survey or poll because they think that others will look unfavorably on their choices, this is referred to as ________________ desirability bias.

Social

Which of these is a characteristic of a "bad" sample?

The sample is not representative of the population being studied.

t distribution

has slightly broader tails than the Z distribution.

The value of the finite population correction factor is always

less than one.

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

normal sampling distribution.

We would conduct a hypothesis test to determine whether or not

sample evidence contradicts H0.

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

small

Assignable variation is caused by

specific events that can usually be identified and eliminated.

We use a calculated sample ______ to make inferences about an unknown population ______.

statistic, parameter

For a hypothesis test on μ when the value of σ is unknown, the value of the test statistic is calculated as ______, provided that we sample from a normal population.

tdf = x−μ0s/√n

Which of the following is considered an estimate?

x^_ = 20

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

xx ± tα/2,df ⋅ s/√n

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

xx ± zα/2 ⋅ σ/√n

The alternative hypothesis typically

contests the status quo, for which a corrective action may be required

Selection bias occurs when

there is a systematic exclusion of certain groups from consideration for the sample.

If X is normally-distributed, we can transform XX into the standard normal random variable as

Z = X−μ/σ/√n

What is the confidence level if α = 0.10?

90%

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

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

6

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

Normal

The Greek letter ______ denotes the level of significance.

α alpha

If the chosen significance level is α = 0.05, then there is a 5% chance of

rejecting a true null hypothesis.

When testing μ and σ is known, H0 can never be rejected if z ≤ 0 for a

right-tailed test.

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

1.645

When a firm inspects the production process to determine at which point the process does not conform to standards, it is applying ______ for statistical quality control.

the detection approach

The significance level is the allowed probability of making

a Type I error.

A sample is

a subset of the population.

The expected value of X^_ is equal to ______.

μ

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.

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

Proportion

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.

If the collected sample data is inconsistent with what is stated in the null hypothesis, which decision is made?

The null is rejected and the alternative is accepted.

How do the tdf and z distributions differ?

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

We can use the finite population correction factor when

n ≥ 0.05N.

The normal distribution approximation for a binomial distribution is valid when

np ≥ 5 and n(1 - p) ≥ 5

For any population proportion p, the sampling distribution of the sample proportion is approximately normally distributed if

np ≥ 5 and n(1 - p) ≥ 5.

Social-desirability bias exists when

opinions that are socially unacceptable are not expressed.

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

p̂

The critical value approach specifies a region of values, called the ______. If the test statistic falls into this region, we reject the ______.

rejection region, null hypothesis

Stratified sampling is preferred to cluster sampling when the objective is

to increase precision.

Suppose you are performing a hypothesis test on μ and the value of σ is known. At the 10% significance level, the critical value(s) for a right-tailed test is (are):

z0.10

We do NOT reject the null hypothesis when the p-value is

≥ α.

When the finite population correction factor is applied to the sample mean, the resulting standard error for the sample mean is equal to

(σ/√n)σ/n√(N−n)/(N−1)(N-n)/(N-1).

Which of the following statements is MOST accurate?

A parameter is a constant although its value may be unknown.

Which of the following statements is MOST accurate?

A statistic is a random variable whose value depends on the chosen random sample.

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.

A Type I error occurs when we

Reject the null hypothesis when it is actually true.

We can generally reduce both Type I and Type II errors simultaneously by

increasing the sample size.

A sampling distribution (select all that apply)

is distribution of a statistic that is calculated from all possible samples of size n from a population. is the same as the probability distribution for a statistic.

We use hypothesis testing to

resolve conflicts between two competing hypotheses regarding a population parameter.

The basic principle of hypothesis testing is to assume that

the null hypothesis is true and see if the sample data contradict this assumption.

If p is the sample proportion from a sample that is large enough, then we can transform the proportion into its standard normal value as

z=p⎯⎯−pp(1−p)n√

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.

A university's athletic program is considering changing its mascot. The SGA administers a survey to assess students' opinions by going to the business building. What type of bias is likely?

Selection Bias

What kind of sampling is more likely to be used by political pollsters who want to ensure that each religious group is represented in the sample?

Stratified random sampling

Which one of the following is true about stratified and cluster sampling?

Stratified sampling provides greater precision.

True or false: If we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

True

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 general, the two approaches that are used for statistical quality control are

acceptance sampling and the detection approach.

The shape of each t distribution depends upon its ______.

degrees of freedom

If the value of the test statistic falls in the rejection region, then the p-value must be

less than α.

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

margin of error.

Control charts were created to

monitor the behavior of a production process.

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

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

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 we were to sample repeatedly from a given population, the average value of the sample means will equal

the population mean.

When performing a hypothesis test on μ when the value of σ is unknown, the test statistic is computed as x−μ0/s÷√n and it follows the

tdf distribution with (n - 1) degrees of freedom.

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 the following to check sample size:

n ≥ 30

When performing a hypothesis test on μ when σ is known, H0 can be rejected for which of the following case?

p-value < α

When H0: μ =12 and xx = 10, the p-value is defined as

p-value = 2 × P(Z ≤ z)

Unlike the mean and standard deviation, the population proportion p is a descriptive summary measure that can be used for data that are ______.

qualitative

Suppose a hypothesis test is conducted at the α=0.05 level, the null would be rejected for p-values between

0 and 0.05