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This is a photo of a plate with a large pile of eggs in the foreground and six slices of toast in the background. There is a small dish of red jam sitting near the toast on the plate.
If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when conducting a hypothesis test. (credit: Chloe Lim)

Chapter objectives

By the end of this chapter, the student should be able to:

  • Classify hypothesis tests by type.
  • Conduct and interpret hypothesis tests for two population means, population standard deviations known.
  • Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.
  • Conduct and interpret hypothesis tests for two population proportions.
  • Conduct and interpret hypothesis tests for matched or paired samples.

Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years.

There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students are interested in whether SAT or GRE preparatory courses really help raise their scores.

You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded.

To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs . Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.


This chapter relies on either a calculator or a computer to calculate the degrees of freedom, the test statistics, and p -values. TI-83+ and TI-84 instructions are included as well as the test statistic formulas. When using a TI-83+ or TI-84 calculator, we do not need to separate two population means, independent groups, or population variances unknown into large and small sample sizes. However, most statistical computer software has the ability to differentiate these tests.

This chapter deals with the following hypothesis tests:

    Independent groups (samples are independent)

  • Test of two population means.
  • Test of two population proportions.

    Matched or paired samples (samples are dependent)

  • Test of the two population proportions by testing one population mean of differences.

Questions & Answers

answer for question 3
Awuah Reply
what are the terminologies in statistics?
Abranti Reply
population sample statistic parameter etc..
the mode of the table class 3_7 8_12 13 _17 frequency 10 25 19
Samah Reply
how touching
i didn't know this app had a chat
I think 25 is higher frequency
compare to 10 and 19
by using formula...?
L+((f1-f0)÷2f1-f0-f2)×h by this formula using ans is 9.8
Me too I think the highest frequency is 25
how is useful
how is stem and leaf plot or display differ from double stem and leaf plot or display
Sebili Reply
What is the variances of 568
Helen Reply
what u asking...
what variance would have a single value..?
variance happened only in a group of values..
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
compare the relative adrantages and disadvantages of mean mediam and made
What is the variances of 258
Helen Reply
what is the sample size if the degree of freedom is 25?
Arthur Reply
degrees of freedom may differ with respect to distribution...so tell which distribution you have selected...?
my distribution is 27
what is degree of freedom?
how to understand statistics
Edwin Reply
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
Halpha Reply
what marriage for 10 years
Ambaye Reply
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
Nayab Reply
how can we find the expectation of any function of X?
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
yes I am. it's been decades since I've been in school.
who are u
is there a private chat we can do
hello how can I get PDF of solutions introduction mathematical statistics ( fourth education) who can help me
can anyone help me
what is probability
zaheer Reply
simply probability means possibility.. definition:Probability is a measure of the likelihood of an event to occur.
fit a least square model of y on x ? what is the regression coefficient ? x : 2 3 6 8 9 10 y : 5 6 7 10 8 11
classification of data by attributes is called
Yamin Reply
qualitative classification
tell me details about measure of Dispersion
Following data provided Class Frequency less than 10 10-20 5 15 10-30 25 12 40 and above Which measure of central tendency would you compute and why?
Nija Reply

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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