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
