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This is a step by step example modeling the process of calculating a hypothesis test for a two population proportion.

Step-by-step example of a hypotheses test for two population proportions (used ex 10.3)

Two types of medication for hives are being tested to determine if medication A is more effective than medication B. One hundred-eighty-eight out of a random sample of 200 adults given medication A did not have hives 30 minutes after taking the medication. One hundred-eighty out of another random sample of 200 adults given medication B did not have hives 30 minutes after taking the medication. Test at the 1% level of significance.

Guidelines Example
State the question: State what we want to determine and what level of significance is important in your decision. We are asked to test the hypothesis that the proportion of adults taking medicine A without hives is more than the proportion of adults taking medicine B without hives after 30 minutes. The significance level is 5%.
Plan: Based on the above question(s) and the answer to the following questions, decide which test you will be performing. Is the problem about numerical or categorical data?If the data is numerical is the population standard deviation known? Do you have one group or two groups?What type of model is this?

We have bivariate, categorical data. We have two independent groups. We have a sample of 200 adults taking medicine A and 200 adults taking medicine B. Our model will be:

P A - P B ~

N ( P A - P B , p ̂ pooled ( 1 - p ̂ pooled ) ( 1 n 1 + 1 n 2 ) )

Hypotheses: State the null and alternative hypotheses in words and then in symbolic form
  1. Express the hypothesis to be tested in symbolic form.
  2. Write a symbolic expression that must be true when the original claim is false.
  3. The null hypothesis is the statement which included the equality.
  4. The alternative hypothesis is the statement without the equality.

Null hypothesis in words: The null hypothesis is that the true proportion of adults helped by medication A is equal to the true proportion of adults helped by medication B.

Null Hypothesis symbolically: H 0 : Proportion p A = p B

Alternative Hypothesis in words: The alternative is that the true proportion of adults helped by medication A is more than the true proportion of adults helped by medication B.

Alternative Hypothesis symbolically: H a : Proportion p A > p B

The criteria for the inferential test stated above: Think about the assumptions and check the conditions.If your assumptions include the need for particular types of data distribution, please insert the appropriate graphs or charts if necessary.

Randomization Condition: The samples are random samples.

Independence Assumption: Since we know that a random sample was taken it is reasonable to assume independence. The likelihood of having the medicine work for one person has no bearing on if it will work for another.

Independent Groups Assumption: It is reasonable to think that the medicine A group and medicine B group recovery rates are independent of each other.

10% Condition: I assume the number of adults in the community where this was done is more than 4000, so the 200 adults in each group is less than 10% of each population.

Success/Failure Condition: Success = no hives Failure = hives (.94)(200) = 188 and (1 - .94)(200) = 12 and (.90)(200) = 180 and (1 - .9)(200) = 20, all values are larger than 10 so the condition is met.

Compute the test statistic:

The conditions are satisfied, so we will use a hypothesis test for two proportions. We will use a z-test.We need the sample percentages, sample sizes, and p-hat pooled.
  • p ̂ A = 188 200 = 0.94; n A = 200;
  • p ̂ B = 180 200 = 0.90; n B = 200
  • p ̂ pooled = 188 + 180 200 + 200 = 0.92
  • z = ( p ̂ A - p ̂ B ) - (0) p ̂ pooled (1 - p ̂ pooled )( 1 n A + 1 n B )
  • = 0.94 - 0.90 0.92(1 - 0.92)( 1 200 + 1 200 )
  • = 0.04 0.19183 = 2.085
Determine the Critical Region(s): Based on your hypotheses are you performing a left-tailed, right-tailed, or two-sided test? I will perform a right-tailed test.

Sketch the test statistic and critical region:

Look up the probability on the table.

Determine the P-value

P(z>2.085) = 1 – P(z<2.085) = 1 – 0.9815 = 0.0185>0.01

State whether you reject or fail to reject the Null hypothesis.

Since the probability is more than the critical value of 1%, we will fail to reject the null hypothesis.
Conclusion: Interpret your result in the proper context, and relate it to the original question. Since the probability is more than 1%, this is not a rare event and the large probability tells us to fail to reject the null hypothesis. There is no evidence against the null hypothesis. There is no reason to believe that medication A is more effective than medication B.

If you reject the null hypothesis, continue to complete the following

Calculate and display your confidence interval for the Alternative hypothesis.

State your conclusion based on your confidence interval.

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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