White (dummy 0)
Red (dummy 1)
.93 + .47*alcohol
(.93 - .26) + .47*alcohol
*REMEMBER: "that predicts _" means that factor is the y-variable!*
This is found using regression analysis.
B.
Interpret the regression coefficients.
Intercept: Pointless to interpr
A. 1. Ho: There is no relationship between x and y.
Ha: There is a relationship between x and y.
Observed
Yes
No
Total
Northeast
Expected
Yes
No
Total
Northeast
102
74
176
2. Significance Level: = .05
3. Test Statistic:
^2 = [(fo - fe)^2/fe]
4. Decision R
Sampling Distributions
Sampling Distributions
When sampling, the resulting sample
statistics or point estimates are random
variables
Like any random variable, they have some
probability distribution
The probability distribution for a sample
statistic is
Measures of Dispersion
Measures of Dispersion
Measures the variability in the data
Common measures of dispersion are the
range, interquartile range, variance,
standard deviation, and the coefficient of
variation
Range
The range measures
the overall sprea
BUS 229
Measures of Central Tendency
Measures of Central Tendency
Mean: The average of the numbers in a data
set
Median: The center value in the data set
(once the data has been ordered from
smallest to largest)
Mode: The observation that occurs most
fr
Confidence Interval for a
Population Proportion
CI for p
The CI for is centered on the point estimate
A z value is always used, since the normal
approximation to the binomial is being used
An estimate of the standard error must be used
since p is unknown
Probability Distributions for
Continuous Random Variables
Continuous Distributions
Continuous Probability distributions can be
represented either graphically or by
mathematical function
Since there are an infinity of possible
values for the random variab
Confidence Intervals
Interval Estimates
An interval estimate is a span of values that
should include an unknown parameter
value. It is defined by two endpoints
Confidence
Confidence is a number between 0 and 100
that reflects the probability (x100%) that
Descriptive Statistics
Descriptive Statistics
Descriptive (Summary) statistics are ways
of summarizing the data
Types of Summary
frequency distributions
graphs
central tendency
dispersion
association
Frequency Distributions
Frequency Distributions are ta
Measures of Association
Examining the relationship between
two variables
Covariance
covariance measures
the association
between two variables
x and y
If the covariance is
positive, the two
variables are directly
related; if negative,
inversely related
(
Sampling
Sampling
People often have questions about
populations (average life of a product,
proportion of people who will vote for a
particular candidate)
It is generally too expensive/time
consuming to survey the entire population
so samples are taken i
Random Variables and
Probability Distributions
Random Variables
Random Variables are variables that may take on
various values due to chance
Random Variables are represented by probability
distributions
Probability distributions represent the values the
R
BUS 229 CP 28 Problems
Multiple Regression Models
1.
A mail-order catalog business that sells personal computer supplies, software, and hardware
maintains a centralized warehouse for the distribution of products ordered. Management is currently
examining
CP 27 Problems
Inference about the Slope, Correlation Coefficient and Estimation of Mean Values and Prediction of
Individual Values
1.
In our previous problem on pet foods and shelf space, the marketing manager used shelf space for pet
food to predict wee
229 CP 25 Problems
Determining the Simple Linear Regression Equation and Using It for Prediction
1.
The marketing manager of a large supermarket chain has the business objective of using shelf
space more efficiently. Toward that goal, she would like to us
229 CP 26 Problems
Measures of Variation and Durbin Watson Test
1.
In an earlier problem, you used the summated rating to predict the cost of a restaurant meal. Perform a
residual analysis for these data (stored in Restaurants2). Evaluate whether the assu
229 CP 23 Problems and Answers
F-Test for the Ratio of Two Variances
1.
2.
3.
4.
Determine the following upper tail critical values of F in each of the following two tailed tests
=0.10, n1 = 16, n2 = 20
1.87
I think there was some information missing for
229 CP 24
Determining Appropriate Two Sample Statistic
1.
Do male and female students study the same amount per week? In a recent year, 58 sophomore
business students were surveyed at a large university that has more than 1,000 business students
each year
229 CP 21
Two Sample Tests and Comparing the Means of Two Related Samples
1.
An experimental design for a paired t test has 25 pairs of identical twins. How many degrees of freedom
are there in this t test? 24 degrees of freedom
2.
Target vs Walmart: who
229 CP 22 Problems
Comparing the Proportions of Two Independent Populations
1.
2.
Let n1 = 100, X1 = 50, n2 = 100, and X2 = 30.
A.
At the the 0.05 level significance, is there evidence of a significant difference between the two
population proportions? Ye
229 CP 20 Problems
Two Sample Tests and Comparing the Means of Two Independent Samples
1.
Assume that you have a sample of n1 = 8, with the sample mean X1 = 42, and a sample standard
deviation S1 = 4, and you have an independent sample of n2 = 15 from ano
229 CP 17 Problems
Hypothesis Testing with the t test
1.
If the sample of n = 16 selected from a normal population,
tstat if you are testing null Hypothesis H0 : =50 ? 2
X
= 56 and S = 12, what is the value of
2.
In problem 1, what are the critical values
229 CP 19 Problems
Z Test of Hypothesis for the Proportion
1.
If, in a random sample of 400 items, 88 are defective, what is the sample proportion of defective items?
0.22
2.
In problem 2, if the null hypothesis is that 20% of the items in a population ar
229 CP 18 Problems
Hypothesis Testing and One Tailed Tests
1.
2.
3.
4.
5.
6.
A.
B.
C.
D.
In a one-tailed hypothesis test where you reject H0 only in the upper tail, what is the p-value if Zstat =
+2.00?
0.0228
In problem 1, what is your statistical decisi
229 CP 16 Problems
Hypothesis Testing Methodology
1.
If you use a 0.05 level of significance in a two-tailed hypothesis test. What decision will you make if Zstat
= -0.76? Do not reject the null hypothesis
2.
If you use a 0.05 level of significance in a t
229 CP 15
Confidence Interval Estimates and Determining Sample Size
1. A manufacturing company produces electric insulators for power lines. If the insulators break while in use,
a short circuit is likely to occur. To test the strength of the insulators,
CP 10
Evaluating Normality
Include screenshots of your graphical and tabular analysis in this word document and upload at the end of
class.
1.
The file SUV.xls contains the overall miles per gallon (MPG) of 2012 small SUVs (n=18). Download this
file from
229 CP 13
Confidence Interval Estimation
X = 85, = 8, n = 64, construct a 95% confidence interval estimate for the population mean, .
83.04 .86.96
X = 125, = 24, n = 24, construct a 99% confidence interval estimate for the population mean, .
2.
112.38 137
229 CP 11
Sampling Distributions
A.
B.
C.
D.
1. Given a distribution of with =100 and =10 , if you select a sample of n = 25, what is the probability
that the sample X is
less than 95? 0.006
between 95 and 97.5? 0.10565
above 102.2? 0.13567
There is a 65%
229 CP 12 Problems
Sampling Distribution of the Proportion
1. In a random sample of 64 people, 48 are classified as successful.
a. Determine the sample proportion, p of successful people. 0.75
b. If the population proportion is 70, determine the standard