Business Stats Final Review

Least squares criterion

(Yi-Yhat)^2

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

(n1 + n2 − 2) degrees of freedom

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

Alternative hypothesis

In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as

(r - 1)(c - 1)

The test for goodness of fit

. is always a one-tail test with the rejection region occurring in the upper tail

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

Becomes smaller

In regression analysis if the dependent variable is measured in dollars, the independent variable

Can be in any units

In conducting a hypothesis test about p1 - p2, any of the following approaches can be used except

Comparing the observed frequencies to the expected frequencies

The interval estimate of the mean value of y for a given value of x is the

Confidence Interval

A measure of the strength of the relationship between two variables is the

Correlation

If the coefficient of determination is a positive value, then the coefficient of correlation must be

Either negative or positive

If we are testing for the equality of 3 population means, we should use the

F Statistic

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

Level of significance

The test statistic F is the ratio

MSR/MSE

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

Residual

In analysis of variance, the dependent variable is called the

Response variable

The multiple coefficient of determination is

SSR/SST

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

Sample size

More evidence against H0 is indicated by

Smaller p values

What is a statistical inference?

Takes the information from a sample to make a statement about the population

In a regression analysis, the variable that is being predicted

The dependent variable

Which of the following is a characteristic of a binomial experiment

The trials are independent

Which of the following descriptive statistics is not measured in the same units as the data

Variance

A multiple regression model has the form = 7 + 2 x1 + 9 x2 As x1 increases by 1 unit (holding x2 constant), is expected to

increase by 2 units

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

a qualitative variable

If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the

alt. hypothesis should say m1-m2<0

The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions

are different than the hypothesized proportions

In regression analysis if the dependent variable is measured in dollars, the independent variable

can be any units

Both the hypothesis test for proportions of a multinomial population and the test of independence employ the

chi squared

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

coefficient of determination

The interval estimate of the mean value of y for a given value of x is the

confidence interva

A measure of the strength of the relationship between two variables is the

correlation coefficient

In regression analysis, the response variable is the

dependent variable

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

dummy variable

An example of statistical inference is

hypothesis testing

In a regression analysis, the variable that is being predicted

is the dependent variable

If a qualitative variable has k levels, the number of dummy variables required is

k − 1

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

matched samples

A least squares regression line

may be used to predict a value of y if the corresponding x value is given

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,

n1 and n2 can be different sizes

The sampling distribution of is approximated by a

normal distribution

Both the hypothesis test for proportions of a multinomial population and the test of independence focus on the difference between

observed frequencies and expected frequencies

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

one dependent and one or more independent variables are related

In regression analysis, an outlier is an observation whose

residual is much larger than the rest of the residual values

The required condition for using an ANOVA procedure on data from several populations is that the

sampled populations have equal variances

The standard error of is the

standard deviation of the sampling distribution of xbar1-xbar2

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

t distribution with 58 degrees of freedom

The properties of a multinomial experiment include all of the following except

the probability of each outcome can change from trial to trial. The probability can NOT change

What is the central limit theorem?

the random variable being observed should be the sum or mean of many independent identically distributed random variables

In a multiple regression model, the variance of the error term ε is assumed to be

the same for all values of the independent variable

The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial

there are three or more outcomes per trial

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

zero