MA141 Midterm Review
TOPIC SUMMARY
A. Picturing Data Sets and the Types of Data:
Type of Data
Representation of Data
Qualitative, Nominal
Bar Chart, Pie Chart
Qualitative, Ordinal
Bar Chart, Pie Chart
Quantitative, Discrete
Bar Chart (also, possibly a Pie
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Winter Term, 2005
STUDENT NUMBER:
WILFRID LAURIER UNIVERSITY
WATERLOO, ONTARIO
Mathematics 141C - Introduction to Applied
Statistical Analysis
Midterm Test
- March 1, 2005
INSTRUCTOR:
R. Elliott
Time Allowed: 90 minutes
Total Value: 100 marks
Number
TYPE I & II ERRORS
TYPE I ERROR
H0 is really TRUE
BUT is incorrectly
REJECTED by the TEST.
TYPE II ERROR
H0 is really FALSE
BUT is incorrectly
ACCEPTED by the TEST.
Example: TESTING
H0:(#(0 vs Ha:(>(0
RIGHT TAIL
"-LEVEL TEST
TYPE I ERROR
[REJECT H0 WHEN T
LEVEL " TESTS OF SIGNIFICANCE
Step 1: Specify ". Step 2: Formulate H0 & Ha. Step 3: Select the appropriate PIVOTAL STATISTIC, [H(G,()-R]. Step 4: Calculate p from the OTS/H(GOBS,(0) value & the R-distribution. Step 5: Compare p with " and draw the appropr
"PACKAGING"
THE EVIDENCE P-VALUE
"STRENGTH OF EVIDENCE" IN FAVOUR OF H0
The probability, p, of obtaining a more extreme value of TS than the one observed (i.e., the OTS) assuming H0 is TRUE. Determined from the OTS value, the TS distribution, R [from RHS
Have we really
Proven
anything about H0 with our
TEST OF SIGNIFICANCE ?
Unfortunately, No!
REJECT H0 Y H0 FALSE '
- and
ACCEPT H0 Y H0 TRUE '
Why Not ?
Suppose we have
REJECTED H0 at LEVEL " (simply because p<"!)
Then, logically we may only conclude th
THE LANGUAGE OF HYPOTHESIS TESTS
HYPOTHESIS
An algebraic expression involving a parameter cfw_( and a number cfw_(0 separated by an equality cfw_= or inequality cfw_<,#,$,> indicating, respectively, a single value [Simple Hypothesis] or set of values [Com