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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.

Note

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

Write a short note on skewness
Saran Reply
and on kurtosis too
Hiren
What is events
Manish Reply
who is a strong man?
Desmond Reply
Can you sir plz provide all the multiple choice questions related to Index numbers.?
Hiren Reply
about probabilty i have some questions and i want the solution
asad Reply
What is hypothesis?
Rosendo Reply
its a scientific guess
ted
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick
what is the d.f we know that how to find but basically my question is what is the d.f? any concept please
asad Reply
Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
d.f >> Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
But we won't get into that. Because degrees of freedom are generally not something you needto understand to perform a statistical analysis—unless you’re a research statistician, or someone studying statistical theory.
Hamzah
And yet, enquiring minds want to know. So for the adventurous and the curious, here are some examples that provide a basic gist of their meaning in statistics.
Hamzah
The Freedom to Vary First, forget about statistics. Imagine you’re a fun-loving person who loves to wear hats. You couldn't care less what a degree of freedom is. You believe that variety is the spice of life Unfortunately, you have constraints. You have only 7 hats. Yet you want to wear a different
Hamzah
hat every day of the week. On the first day, you can wear any of the 7 hats. On the second day, you can choose from the 6 remaining hats, on day 3 you can choose from 5 hats, and so on.
Hamzah
When day 6 rolls around, you still have a choice between 2 hats that you haven’t worn yet that week. But after you choose your hat for day 6, you have no choice for the hat that you wear on Day 7. You must wear the one remaining hat. You had 7-1 = 6 days of “hat” freedom—in which the hat you wore
Hamzah
That’s kind of the idea behind degrees of freedom in statistics. Degrees of freedom are often broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters.
Hamzah
please help me understand binomial distribution
Nnenna Reply
binomial distribution and poisson both are used to estimate the number of successes probable against the. probable failures. the difference is only that BINOMIAL dist. is for discrete data while POISSON is used for continuous data.
Salman
What do you need to understand?
Angela
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution
Hamzah
poisson distribution is also for discrete data set. The difference is when the probability of occurring an event is very little and the sample size is extra large then we use poisson distribution.
Neil
Neil yes you got it and very interested answer you gave
jamilu
How to know if the statement is 1 tail or 2 tail?
Coleen Reply
1 tail if greater than pr less than.2 tail if not equal.
Jojo
in such a case there is no sufficient information provided to develop an alternative hypothesis and we can decide between only two states i.e either the statement is EQUAL TO or NOT EQUAL TO under given conditions
Salman
for 1tail there must be certain criteria like the greater than or less than or some probability value that must be achieved to accept or reject the original hypothesis.
Salman
for example if we have null hypothesis Ho:u=25 Ha:u#25(not equal to 25) it would be two tail if we say Ho:u=25 Ha:u>or Ha:u<25 it would be consider as one tail I hope you will be understand #Coleen
Shabir
yes its true. now you have another problem. so share.
ibrar
what is z score
Esperanza Reply
How to find z score through calculator
Esperanza
Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another. The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data s
Hamzah
what are random number
Saif Reply
how to compute the mean with a long method
Fria Reply
there is a shortcut method for calculating mean long methid doesn't make any sense.
Neil
what are probability
Saif
probability mass function
Saif
probability density function
Saif
there are many definitions of probability. which one is, the ratio of favourable outcomes & total outcomes.
suhail
distribution used for modeling/(find probabilities) of discrete r.v. is called p.m.f
suhail
distribution used for modeling/(find probabilities) of continued r.v, called p.d.f
suhail
lets use short method using calculator.... store yo data n smply get your mean
Flavian
if 1 calorie =4.12 kj, what is the total kj value of this dish
Jacqueline Reply
summation of values of x1 x2 x3 ,,,,xn divided by total number n if it is with frequency its like this summation of values of x1f1+x2f2+x3f3+xnfk divided by summation of frequencies like f1+f2+f3+fk
farah 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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