what is entimology

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briefly describe entomology as per the native studies

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WEEK 6 – HOMEWORK 6: LANE CHAPTERS, 11, 12, AND 13; ILLOWSKY CHAPTERS 9, 10
INTRODUCTION TO HYPOTHESIS TESTING
WHAT IS A HYPOTHESIS TEST?
Here we are testing claims about the TRUE POPULATION’S STATISTICS based on SAMPLES we have taken. The most
common statistic of interest is of course the POPULATION MEAN (µ). But, we can also test its VARIANCE and its
STANDARD DEVIATION. (We can also compare TWO or more means to see if there are significant differences.
We must have a basic hypothesis, referred to as the NULL Hypothesis (Ho) and an ALTERNATE Hypothesis (Ha).
Our NULL ( and ALTERNATE) Hypotheses can take three forms:
(1) Ho:

µ

< some number; Ha: µ > that number (< is “less than or equal to” and > is “greater than or equal to” ),

(2) Ho:

µ

(3) Ho:

µ = some number;

> some number; Ha:
Ha

µ

< that number , or

µ ≠ that number ;

(≠ means “not equal to”)

NOTE THAT Ho MUST HAVE THE “EQUALS” IN IT WHEREAS Ha NEVER DOES.
(1) Is referred to as a “ONE-TAILED TEST TO THE LEFT”
(2) Is a “ONE-TAILED TEST TO THE RIGHT”
(3) Is a “TWO-TAILED TEST”
NEXT, we need to decide what level of significance, i.e.(how sure we want to be about our hypothesis. This is where α
comes in again. Do we want to test at the 10%, 5% or 1% level of significance? Another wrinkle is that for the TWOTAILED test, since our value could be greater OR less than some number, we use α /2 for each extreme, so for 10% it’s
5% (0.050) at each end (tail of the curve), for 5% it’s 2.5% (0.0250) at each end, and for 1% it’s 0.5% (0.0050) at the
ends. You have heard about this kind of split before with confidence intervals, but think about it. Here is a graphical
display of all this:

As you can see, there is a CRITICAL z-VALUE for each of these test depending on the significance level alpha (α) or α/2.
In HW4 questions 1 and 2, you found the critical z-values for alpha’s of 1%, 5% and 10%, which would work for the onetailed tests. For the two tailed tests we need to split these alphas (α/2) and find the critical z-values (at the positive and
negative tails of the graph) So, for an α of 1% (0.0100) it would be α/2 or 0.005 in the left tail (negative z-value) = -2.575
and for the far right tail (0.005 in that tail) we would have to find the z-value for an area to the LEFT of 99.5% (0.9950)
and this is +z = +2.575

Continuing on, for an α of 5% for a two-tailed test the z-values for α/2 would correspond to areas under the curve of
0.0250 at each end. The far left tail would have a negative z-value of -1.96 (see picture above) and the far right tail
would have a positive z-value of +1.96 that in the Table represented an area of 97.5% (0.9750) to the LEFT.
Lastly, for an alpha of 10%, hence an α/2 at both ends of 5% (the two-tailed test), the negative z-value would be -1.645.
The positive z-value marking the upper 5% (Table value from 95% to the left) is +1.645.
SO, FOR YOUR USE IN ALL HYPOTHESIS TEST (AND WORKS FOR CONFIDENCE INTERVALS TOO) HERE IS A TABLE OF THE
CRITICAL Z-VALUES FOR THE VARIOUS LEVELS OF SIGNIFICANCE (ALPHA’s) MOST COMMONLY USED.
ALPHA (α)

-Z-value
+Z-value
ALPHA/2
-Z-value
+Z-value
(LEFT tail) (RIGHT tail)
(α/2)
(LEFT tail)
(RIGHT tail)
1% (0.0100)
-2.33
+2.33
0.5% (0.0050)
-2.575
+2.575
5% (0.0500)
-1.645
+1.645
2.5% (0.0250)
-1.96
+1.96
10% (0.1000)
-1.28
+1.28
5% (0.0500)
-1.645
+1.645
(For those in the NAVY the left and right colors are for PORT and STARBOARD and the history of these terms is
interesting (“google” them).
HYPOTHESIS TESTING:
1. WRITE OUT YOUR NULL (Ho) AND ALTERNATE (Ha) HYPOTHESES, MAKING SURE THE NULL INCLUDES AN
“EQUALS”.
2. DECIDE ON THE LEVEL OF SIGNIFICANCE (α) YOU WANT (OR ARE TOLD TO USE-BUT IF NOT TOLD ASSUME 5%)
3. SOMETIMES THE LEVEL IS REFERRED TO AS 95% (FOR 5%), 90% FOR (10%) AND 99% FOR (1%). THIS IS JUST TO
CONFUSE US.
4. USING THE FORMULAS PROVIDED (IN THE TEXTS) CALCULATE THE TEST STATISTI...


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