Chapter 7-9 QBA Multiple Choice

The exact spread of the t distribution depends on the _________.

Number of degrees of freedom

If a hypothesis is not rejected at a 5% level of significance, it will

also not be rejected at the 1% level

As standard deviation increases, sample size _____________ to achieve a specified level of confidence.

increases

The level of significance is the

maximum allowable probability of Type I error

Assuming the same level of significance α, as the sample size increases, the value of ta/2___________ approaches the value of zα/2.

Always

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

1.487

According to the Central Limit Theorem, if a sample size is at least _____, then for most sampled populations, we can conclude that the sample means are approximately normal.

30

A "Yes or No" question is _____________.

Dichotomous

Which of the following hypotheses applies to a situation where action must be taken both when H0 cannot be rejected and when H0 can be rejected?

H0: u = u0

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

H0: µ = 12 Ha: µ not equal to12

In determining the sample size to estimate a population proportion, as p approaches .5, the calculated value of the sample size ______________

Increases

As the sample size ______________, the variation of the sampling distribution of the sample mean ___________.

Increases, decreases

When the level of confidence and the sample size remain the same, a confidence interval for a population mean μ will be ________________ when the sample standard deviation s is small than when s is large.

Narrower

When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be ______________ a confidence interval for a population mean based on a sample of n = 50.

Narrower than

The level of significance can be any

None of the answers is correct.

Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality:

Population A will require a larger sample size

__________ sampling is defined as sampling where we know the chance that each element in the population will be included in the sample.

Probability

Methods for obtaining a sample are called:

Sample designs

A confidence interval for the population mean is an interval constructed around the ____________.

Sample mean

Methods for obtaining a sample are called

Sampling designs.

Nonoverlapping groups in random sampling of a population are called:

Strata

There is little difference between the values of tα/2 and zα/2 when:

The sample size is large

When the population is normally distributed, population standard deviation σ is unknown, and the sample size is n = 15; the confidence interval for the population mean μ is based on:

The t distribution

As a general guideline, the research hypothesis should be stated as the

alternative hypothesis

Assuming the same level of significance α, as the sample size increases, the value of ta/2 ___________ approaches the value of zα/2.

always

Consider a sampling distribution formed based on n = 3. The standard deviation of the population of all sample means is ______________ less than the standard deviation of the population of individual measurements σ.

always

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is

approximately normal for large sample sizes

sample is used to estimate the population parameter

becomes wider

The ability of an interval estimate to contain the value of the population parameter is described by the

confidence level

The confidence associated with an interval estimate is called the

confidence level

In hypothesis testing, the __________ is a number that establishes the boundary of the rejection region

critical value

As the sample size increases, the margin of error

decreases

As the sample size increases, the variability among the sample means

decreases

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

degrees of freedom

What is a Type II error?

failing to reject a false H0

In order to test the hypotheses H0: µ ≤ 100 Ha: µ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is

greater than or equal to z sub alpha

The practice of concluding "do not reject H0" is preferred over "accept H0" when we

have not controlled for the Type II error

An example of statistical inference is

hypothesis testing

For nonnormal populations, as the sample size (n) ___________________, the distribution of sample means approaches a(n) ________________ distribution.

increases, normal

When the hypotheses H0: µ \ge≥ 100 Ha: µ < 100 are being tested at a level of significance of \alphaα, the null hypothesis will be rejected if the test statistic z is

less than or equal to -z(alfa)

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve

less than or equal to the test statistic

If the cost of a Type I error is high, a smaller value should be chosen for the

level of significance

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

level of significance

The Central Limit Theorem states that as the sample size increases, the distribution of the sample ____________ approaches the normal distribution.

means

Since the sample size is always smaller than the size of the population, the sample mean must

none is correct

hypothesis test in which rejection region is in one tail of the sampling distributio

one-tailed test

probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

p-value

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

p-value less than or equal to alfa

The general form of an interval estimate of a population mean (as well as that of a population proportion) is the _____ plus and minus the _____.

point estimate, margin of error"

If we wish to estimate a population parameter by using a sample statistic, we are using ___________.

point estimation

What is a Type I error?

rejecting a true H0

The level of significance in hypothesis testing is the probability of

rejecting a true null hypothesis

In point estimation, data from the

sample is used to estimate the population parameter

The degrees of freedom associated with a t distribution are a function of the

sample size

The standard deviation of all possible values is called the

standard error of the mean

Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean?

t distribution

In hypothesis testing if the null hypothesis is rejected,

the alternative hypothesis is accepted

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

the correct decision has been made

In hypothesis testing, the alternative hypothesis is

the hypothesis concluded to be true if the null hypothesis is rejected

In developing an interval estimate of the population mean, if the population standard deviation is unknown

the sample standard deviation and t distribution can be used

hypothesis test in which rejection region is in both tails of the sampling distribution

two-tailed test

The error of rejecting a true null hypothesis is

type I error

If a hypothesis test leads to the rejection of the null hypothesis, a

type I error may have been committed

The t distribution approaches the _______________ distribution as the sample size ___________.

z, increases