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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
Wellington
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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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