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This module is the complementary teacher's guide for the "Hypothesis Testing: Two Population Means and Two Population Proportions" chapter of the Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

The comparison of two groups is done constantly in business, medicine, and education, to name just a few areas. You can start this chapter by asking students if they have read anything on the Internet or seen on television any studies that involve two groups. Examples include diet versus hypnotism, Bufferin® with aspirin versus Tylenol®, Pepsi Cola® versus Coca Cola®, and Kellogg's Raisin Bran® versus Post Raisin Bran®. There are hundreds of examples on the Internet, in newspapers, and in magazines.

This chapter covers independent groups for two population means and two population proportions and matched or paired samples. The module relies heavily on technology. Instructions for the TI-83/84 series of calculators are included for each example. If you and your class are interested, the formulas for the test statistics are included in the text.

Doing problems 1 - 10 in the Homework helps the students to determine what kind of hypothesis test they should perform.

Matched or paired samples

A course is designed to increase mathematical comprehension. In order to evaluate the effectiveness of the course, students are given a test before and after the course. The sample data is:

Before Course 90 100 160 112 95 190 125
After Course 120 95 150 150 100 200 120

Two proportions, independent groups

Suppose in the last local election, among 240 30-45 year olds, 45% voted and among 260 46-60 year olds, 50% voted. Does the data indicate that the proportion of 30-45 year olds who voted is less than the proportion of 46-60 year olds? Test at a 1% level of significance.

    Firm a:

  • N A = 20 size 12{N rSub { size 8{A} } ="20"} {}
  • S A = $ 100 size 12{S rSub { size 8{A} } =$"100"} {} X A ¯ = $ 1500 size 12{ {overline {X rSub { size 8{A} } }} =$"1500"} {}

    Firm b:

  • N B = 22 size 12{N rSub { size 8{B} } ="22"} {}
  • S B = $ 200 size 12{S rSub { size 8{B} } =$"200"} {} X B ¯ = $ 1900 size 12{ {overline {X rSub { size 8{B} } }} =$"1900"} {}

Test the claim that the average price of Firm A's laptop is no different from the average price of Firm B's laptop.

Calculator instructions

If you use the TI83/84 series, the functions are located in STATS TESTS. The function for two proportions is 2-PropZTest, the function for two means is 2-SampTTest if the population standard deviations are not known and 2-SampZTest if the population standard deviations are known (highly unlikely). The function for matched pairs is T-test (the same test used for test of a single mean) because you combine two measurements for each object into a single set of "difference" data. For the function 2-SampTTest, answer "NO" to "Pooled."

Assign practice

Have students do the Practice 1 and Practice 2 collaboratively in class. These practices are for two proportions and two means. For matched pairs, you could have them do Example 10-7 in the text.

Assign homework

Assign Homework . Suggested homework problems: 1 - 10, 11, 13, 15, 17, 19, 23, 25, 31, 39 - 52.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
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Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
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Cesar
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Uday
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Collaborative statistics teacher's guide. OpenStax CNX. Oct 01, 2008 Download for free at http://cnx.org/content/col10547/1.5
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