stats final chapter 8, 9, and 10

suppose that, after using the sample size formula, you find n=83.25. what sample size would you use?

84

which of the following is a point estimate?

_ x

define the sampling distribution of the sample mean

a probability distribution of all possible sample means given sample size

What is a confidence interval?

a range of values, created using a sample, within which a population parameter has a certain probability occurring.

which of the following statements is the best definition of a point estimate?

a sample statistic that estimates a population parameter

what is the best definition of the null hypothesis Ho?

a statement about a population parameter to be tested using sample measures

what is a test statistic?

a value, determined from sample information, used to test the null hypothesis

the probability of rejecting a true null is known as which of the following

a, type 1 error

when we speak of an "80% confidence interval" what are we referring to?

an 80% probability that a parameter will be within a specified interval

describes a random process that could be used to create a simple random sample

assigning numbers to members of the population and drawing the numbers out of a hat

why is it necessary to apply the finite population correction factor when a sample is significant part of the population?

if a sample is a larger part of the population, it will give a better estimate

which of the following statements correctly describes the role of the population standard deviation, o, in creating a confidence interval for the population mean?

if o is known, we can use it to calculate the confidence interval -if o is not known, we estimate it using the sample standard deviation

what is the effect of the finite correction factor on a sample based estimate?

it makes the estimate more precise (narrower) for larger samples

what is the effect of the finite population correction factor on a sample based estimate?

it makes the estimate more precise (narrower) for larger samples

.why is it important to know the population standard deviation when estimating the population mean?

knowing o lets us use the standard normal distribution to construct a confidence interval.

how does sample size affect the width of the confidence interval for the population mean

larger sample sizes result in narrower intervals

how does the standard deviation of the population affect the width of the confidence interval for the population mean?

larger values of the population standard deviation result in wider intervals

if we reject a false null hypothesis, what type of error would we be making?

no error is made

which of the following must be true so that the standard normal distribution can e used to construct a confidence interval for the population proportion?

nπ≥5 and n(1-π)≥5

why is systematic sampling sometimes used in place of simple random sampling?

sometimes its difficult to assign random numbers

for a given confidence level, how does a confidence interval calculated using the t-value compare to one calucated using the z-value?

the confidence interval from the t-value is wider

statement describes sampling error

the difference between a sample statistic and its corresponding population parameter

describes the relationship between the mean of the sample means and the population mean

the mean of the sample means equals the population mean

what characteristic of a population requires the use of stratified random sampling to avoid bias

the population is clearly divided into groups based on some characteristics

what is the meaning of "level of significance" in the context of hypothesis testing?

the probability of rejecting the null hypothesis when it is true

what is meant by the term "level of confidence"

the probability that a parameter will be found within the confidence interval

what is the p-value

the probability that a sample value would be as far or further from the expected value, given that the null hypohthesis is true

The Central Limit Theorem describes an expected distribution shape. what is correct ?

the sampling distribution of the sample mean is nearly normal

what is a decision rule in the context of hypothesis testing?

the specific conditions under which the null hypothesis is to be rejected

what is true regarding parameters and statistics?

u is a parameter and s^2 is a statistic

the binomial conditions must be met before we can develop a confidence interval for a population proportion. which two of the following are binomial conditions?

we can define two outcomes, success and failure - the probability of success is the same for all trials

when is it inappropriate to use systematic random sampling?

when the order of the items in the population is related to some particular characteristic

sample error expression

xbar-upside down u

what are features of the central limit theorem?

-for large sample size, the distribution of sample means is independent of the shape of the population -it describes the sampling distribution of the sample mean -the distribution shape is approximately normal

which of the following are essential elements of hypothesis testing?

-it makes use of sample data - it uses probability theory to determine if a hypothesis is a reasonable statement

economics plays a role in the sampling process. which statements correctly describe this relationship?

-larger sample cost more, and increasing size gives diminishing marginal returns in accuracy -the cost of studying an entire population be prohibitive

choose the two statements that correctly reflect traditional usage of significance level ins statistical research

-quality control uses 1% level of significance -consumer research uses a 5% significance

we wish to test Ho:u<or equal to 12 and H1:u> 12 at the .05 level of significance. what is correct

-reject HO IF Z>-1.65 -Fail to reject Ho if z<1.65

identify the steps required in taking a systematic random sample.

-select every sth member of the population from the starting point. -divide the population size by the sample size to find k -select a random starting point

which of the following distinguish systematic random sampling from simple random sampling?

-systematic random sampling uses only one random choice, instead of several -systematic random sampling is quicker and easier

characteristics of the set of sample means

-the distribution of sample means is nearly normal if the sample size is large -the dispersion of the sample means is narrower than the population dispersion -the mean of the sample means equals the mean of the population

which of the following items are valid considerations in the choice of sample size?

-the margin of error the researcher will tolerate -the population dispersion -the desired level of confidence

accurately describe p value

-the null is rejected when the p value is less than a -if we reject the null, it is the probability of making a Type 1 error

accurate statements of the null hypothesis include

-the purpose of the test is to prove the null hypothesis is false. -the term null refers to no significant difference -designated Ho

select all that are accurate descriptions of the null hypothesis

-the purpose of the test is to prove the null hypothesis is false. -the term null refers to no significant difference -the null hypothesis is designated Ho

which of the factors listed below determines the width of a confidence interval?

-the size of the standard error -the chosen level of confidence

there are two conditions under which we can assume that the sample means follow a normal distribution. what are they?

-we don't know the population distribution, but the sample size is 30 or larger -we know the population is normally distributed

if there is no estimate of the population proportion, what value should be used?

.5

Knowing the population standard deviation. which two of the following could be used to estimate the population standard deviation?

1/6 of the population range the sample standard deviation from the pilot study.

describe the relationship between a population and a sample

- a sample statistic is probably not exactly the same as the corresponding population characteristic -a sample is a subset of the population -samples are used to estimate population characteristics

descriptions of the sampling distribution of the sample mean

- it is a probability distribution of all possible sample means -it is a distribution of means from samples of all one size

which of the following considerations require a larger sample size?

-a smaller margin on error -a higher level of confidence

which of the following statements accurately describes the alternate hypothesis?

-also called the research hypothesis -it is accepted as a consequences of the null hypothesis being rejected

describe valid reasons to use a sample instead of evaluating a much larger population

-contacting the whole population owl be marginally more accurate than a sample -contacting the entire population would be time consuming

in constructing a confidence interval to estimate the population mean from a sample, which of the following steps are necessary only when o is not known?

-find the sample standard deviation -find the t-value for the proper distribution, based on the sample size.

what is correct procedure when you want to do a test of the population mean but the population standard deviation is unknown?

-find the sample standard deviation and use it as an estimate for the population standard deviation -the t-distribution is used in place of the z-distribution, assuming a normal population

when the population standard deviation is known, the confidence interval for the population mean is based on the

z-static