<< Chapter < Page Chapter >> Page >
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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics using spreadsheets' conversation and receive update notifications?