BUS245 FINAL EXAM

p-value

*favored by most researchers and practitioners *virtually every statistical software package the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample under the assumption that the null hypothesis is true

confidence interval

*sometimes used as an alternative method for conducting a two-tailed hypothesis test. given that we conduct the hypothesis test at the a-sig. lvl., we can use the sample data to determine corresponding 100(1-a)%

Formulating the competing hypothesis

1.) identify the relevant population parameter of interest 2.) determine whether it is a one or two-tailed test 3.) include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

statiscal inference concerning the mean difference based on matched-pairs sampling requires one of two conditions:

1.) the sample size n >(or equal to) 30 2.) both X1 and X2 are normally distributed

goodness of fit measure includes:

1.) the standard error of the estimate 2.)the coefficient of determination 3.)the adjusted coefficient of determination

alternative hypothesis p-value table

Alternative Hypothesis p-value: HA:μ>μ0HA:μ>μ0 (Right-tail probability) P(Z≥z)PZ≥z HA:μ<μ0HA:μ<μ0 (Left-tail probability): P(Z≤z)PZ≤z HA:μ≠μ0HA:μ≠μ0 (Two-tail probability): 2P(Z≥z)2PZ≥z if z>0z>0 or 2P(Z≤z)2PZ≤z if z<0

reject null hypothesis

If sample evidence is INCONSISTENT, we REJECT the null hypothesis

when examining the difference between two population means, if the populations cannot be assumed normal, then (X1-X2) is approximately normal if

N1 and N2 are greater than or equal to 30

statistical inference

The process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population. (U1-U2)

null hypothesis (H0)

a default state of nature of status quo

A particular personal trainer works primarily with track and field athletes. She believes that, on average, her clients run faster after going through her program for 6 weeks. How might she test that claim?

a matched-pairs comparison

method of least squares

also known as ordinary least squares (OLS) a regression technique for fitting a straight line whereby the error sum of squares is minimized

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

always the same

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

both approaches lead to the same conclusion

a pooled estimate of the common variance between two populations is used when

both populations are assumed to have the same population variance

an important final conclusion to a statistical test is to

clearly interpret the results in terms of the initial claim

independent random samples are

completely unrelated to one another

alternative hypothesis (HA)

contradicts the default state or status quo specified in the null hypothesis

coefficient of determination

denoted as R2 never decreases as more explanatory variables to the linear regression

matched-pairs sampling is an example of

dependent sampling

the variables that influence the response variable; also called the independent, predictor, control or regressor variables

explanatory variables

True or False: in the critical value approach, if the value of the test statistic does not fall within the rejection then we reject the null hypothesis

false

hypothesis testing

first assume that the null hypothesis is true and then determine if the sample evidence contradicts this assumption

suppose you want to perform a test to compare the mean GPA of all freshman with the mean GPA of all sophomores in a college and have no other data than the students' GPA. What type of sampling is required for this test?

independent sampling with quantitative data

a confidence interval for the difference between two population proportions p1-p2 follow the general format of a point estimate

margin of error

regression sum of squares

measures the explained variation in the response variable

multiple linear regression model

more than one explanatory variable is used to explain the variability in the response variable

the normal distribution approximation for a binomial distribution is valid when

np > (or equal to) 5 and n(1-p)> (or equal to) 5

The two competing hypotheses used in hypothesis testing are called the _____ and the _______.

null and alternative

Type II Error

occurs when the decision is made to accept the null hypothesis when it is actually false

simple linear regression model

one explanatory variable is used to explain the variability in the response variable

as a point estimate of the population proportion, we calculate

p

In a hypothesis test, U0 and P0 are hypothesized values of the ____ mean and the ____ proportion, respectively.

population, population

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

qualitative

a statistical method for analyzing the relationship between variables

regression analysis

when using the p-value

reject the null hypothesis if the p-value < a accept the hypothesis if the p-value is greater than or equal to a

if 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

when testing u and std.dev. , Ho can never be rejected if z is less than or equal to 0 for a

right-tailed test

If the standard deviation is unknown, it can be estimated by using ____

s

test statistic

sample based measure when testing hypothesis

In inferential statistics, we use ____ information to make inferences about an unknown ____ parameter.

sample, population

residual e

the difference between the observed value and the predicted value of the response variable e=y-^y

two-tailed hypothesis test

the null hypothesis can be rejected on both sides of the hypothesized value of the population parameter *defined when the alternative hypothesis includes the does not equla symbol

when constructing a confidence interval for the difference between two population means, the margin of error equals

the standard error multiplied by z(a/2) or t (a/2,df)

Type I Error

this occurs when the decision is made to reject the null hypothesis when it is actually true

True or False: We choose a value for a before conducting a hypothesis test

true

True or False: the optimal values of type 1 and type 2 errors require compromise in balancing the costs of each type of error

true

true or false: for a given sample size N, a type 1 error can only be reduced at the expense of a higher type 2 error.

true

independent random samples

two or more random samples are considered independent if the process that generates one sample is completely separate from that process that generates the other sample

B (beta) denotes

type 2 error

adjusted R2

used to compare competing linear regression models with different numbers of explanatory variables; the higher the adjusted R2, the better the model

we calculate a pooled estimate of the common variance by

using weighted averages of sample variances

matched-pairs sampling

when a sample is matched or paired in some way *sometimes referred to as the mean difference or uD where D=X1-X2 and X1/X2 are matched in a pair.

in most applications, the hypothesized difference between two population means is

zero

critical value approach

attractive when a computer is unavailable and all calculations must be done by hand *the value that separates the rejection region from the non-rejection region

in order to select the preferred model, we need to examine

goodness of fit measure

accept null hypothesis

if the sample evidence is solid and consistent, we will ACCEPT the null hypothesis

we can generally reduce both type 1 and type 2 errors simultaneously by

increasing the sample size

a (alpha) denotes

type 1 error

a confidence interval for the mean difference uD follows the general format of a point estimate

margin of error

a specific type of dependent sampling when the samples are paired in some way

matched-pairs

if the same individuals are evaluated before and after a weight loss program, this is an example of

matched-pairs sample

for matched pairs sampling, the parameter of interest is referred to as the

mean difference

if the hypothesized difference between two population proportions is zero, then the standard error can be improved by computing a

pooled estimate of the proportion

The expected value of the sampling distribution of P is the ____

population proportion

when performing a hypothesis test on u when the value of the std.dev. is unknown, the tyest statistic is computed as x-Uo/s/(sq.rt)n and it follows the

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

significance level

the allowed probability of making a type 1 error; denoted as alpha or 100%a

one-tailed hypothesis test (right-tailed or left-tailed)

the null hypothesis is only rejected one one side of the hypothesized value of the population parameter *will be denoted with a greater or less than symbol or greater, less than, or equal to symbol

response variable

the variable that is influenced by the explanatory variable(s). It also is called the dependent, explained, predicted or regressand variable

when testing whether two populations proportions differ, we use a

two-tailed test

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

z= p-Po/ (square root) Po(1-Po)/N