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Hypothesis Testing: Two Population Means and Two Population Proportions: Teacher's Guide

Module by: Dr. Barbara Illowsky, Susan Dean

Summary: 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.

Example 1: 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

Example 2: 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:

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

Firm B:

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

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