<< Chapter < Page Chapter >> Page >

Suppose a consumer group suspects that the proportion of households that have three cell phones is 30%. A cell phone company has reason to believe that the proportion is 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with theresult that 43 of the households have three cell phones.

Set up the Hypothesis Test:

H o : p = 0.30 H a : p 0.30

Determine the distribution needed:

The random variable is P ' = proportion of households that have three cell phones.

The distribution for the hypothesis test is P ' ~ N ( 0.30 , (0.30) (0.70) 150 )

The value that helps determine the p-value is p ' . Calculate p ' .

p ' = x n where x is the number of successes and n is the total number in the sample.

x = 43 , n = 150

p' = 43 150

What is a success for this problem?

A success is having three cell phones in a household.

What is the level of significance?

The level of significance is the preset α . Since α is not given, assume that α = 0.05 .

Draw the graph for this problem. Draw the horizontal axis. Label and shade appropriately.

Calculate the p-value.

p-value = 0.7216

Make a decision. _____________(Reject/Do not reject) H 0 because____________.

Assuming that α = 0.05, α < p-value . The Decision is do not reject H 0 because there is not sufficient evidence to conclude that the proportion of households that have three cell phones is not 30%.

The next example is a poem written by a statistics student named Nicole Hart. The solution to the problem follows the poem. Notice that the hypothesis test is for a singlepopulation proportion. This means that the null and alternate hypotheses use theparameter p . The distribution for the test is normal. The estimated proportion p ' is the proportion of fleas killed to the total fleas found on Fido. This is sample information.The problem gives a preconceived α = 0.01 , for comparison, and a 95% confidence interval computation. The poem is clever and humorous, so please enjoy it!

Hypothesis testing problems consist of multiple steps. To help you do the problems, solution sheets are provided for your use. Look in the Table of Contents Appendix for the topic "Solution Sheets." If you like, use copies of the appropriate solution sheet for homework problems.

My dog has so many fleas, They do not come off with ease.As for shampoo, I have tried many types Even one called Bubble Hype,Which only killed 25% of the fleas, Unfortunately I was not pleased.I've used all kinds of soap, Until I had give up hopeUntil one day I saw An ad that put me in awe.A shampoo used for dogs Called GOOD ENOUGH to Clean a HogGuaranteed to kill more fleas. I gave Fido a bathAnd after doing the math His number of fleasStarted dropping by 3's! Before his shampooI counted 42. At the end of his bath,I redid the math And the new shampoo had killed 17 fleas.So now I was pleased. Now it is time for you to have some funWith the level of significance being .01, You must help me figure outUse the new shampoo or go without?

Set up the Hypothesis Test:

H o : p = 0.25 H a : p > 0.25

Determine the distribution needed:

In words, CLEARLY state what your random variable X or P' represents.

P' = The proportion of fleas that are killed by the new shampoo

State the distribution to use for the test.

Normal: N ( 0.25 , ( 0.25 ) ( 1 - 0.25 ) 42 )

Test Statistic: z = 2.3163

Calculate the p-value using the normal distribution for proportions:

p-value = 0.0103

In 1 – 2 complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the proportion is 0.25), then there is a 0.0103 probability that the sample (estimated) proportion is 0.4048 ( 17 42 ) or more.

Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Normal distribution graph of the proportion of fleas killed by the new shampoo with values of 0.25 and 0.4048 on the x-axis. A vertical upward line extends from 0.4048 to the curve and the area to the left of this is shaded in. The test statistic of the sample proportion is listed.

Compare α and the p-value:

Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using COMPLETE SENTENCES.

alpha decision reason for decision
0.01 Do not reject H o α p-value

Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of fleas that are killed by the new shampoo is more than 25%.

Construct a 95% Confidence Interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the Confidence Interval.

Normal distribution graph of the proportion of fleas killed by the new shampoo with values of 0.26, 17/42, and 0.55 on the x-axis. A vertical upward line extends from 0.26 and 0.55. The area between these two points is equal to 0.95.

Confidence Interval: ( 0.26 , 0.55 ) We are 95% confident that the true population proportion p of fleas that are killed by the new shampoo is between 26% and 55%.

This test result is not very definitive since the p-value is very close to alpha. In reality, one would probably do more tests by giving the dog another bath after the fleas have had a chance to return.

Questions & Answers

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.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary statistics' conversation and receive update notifications?

Ask