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This is a picture of a Dalmation dog covered in black spots. He is wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain in the foreground.
You can use a hypothesis test to decide if a dog breeder’s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)

Chapter objectives

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

  • Differentiate between Type I and Type II Errors
  • Describe hypothesis testing in general and in practice
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
  • Conduct and interpret hypothesis tests for a single population proportion.

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called " hypothesis testing ." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analyses of the data, to reject the null hypothesis.

In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:

  1. Set up two contradictory hypotheses.
  2. Collect sample data (in homework problems, the data or summary statistics will be given to you).
  3. Determine the correct distribution to perform the hypothesis test.
  4. Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
  5. Make a decision and write a meaningful conclusion.

Note

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See Appendix E .

Questions & Answers

According to my understanding, statistics are numerical data or information presented in charts or graphs
Kristen Reply
thanks
Said
what is statistics
Elisha Reply
how to find critical angle
Muhammad Reply
what is statistics ?
Samad
Statistics is deal with the collection, analysis, interpretation, presentation of data to drawn out conclusions.
Ajao
collection presentation analysis interpretation Kia he sir
Samad
In my own perspective statistics is deal with the collection, analysis, interpretation, presentation of data before will drawn our conclusions
Ajao
thank you sir pragaph bejo
Samad
In simple way it is the technique of problem solving by providing probabilistic answer to questions otherwise whose exact answer is not possible..besides it is the support to every subject you study.
being
data
Deng
Data is information that has been translated into a form that is efficient for movement or processing
Mansour
group the scores below into a class interval of seven and obtain the following: 1.. i..class interval ii..tally iii..frequency iv..mid point v...cummulative frequency less than vi..cummulative frequency more than vii..relative frequency viii...relative percentage
Icecool
2..draw a histogram and frequency polygon to sick it the statistical table
Icecool
20,30,39,25,50,26,39,32,43,20,30,40,50,10,16,12,19,31,32,26,29,27,28,42,63,48,11,26,35,36,37,38,39,39,35,29,53,37,32,24,36,43,48,42,51,37,39,39,24,7,8,13,62,52,69,68,37,38,39,40,41,39,54
Icecool
2.draw a histogram and frequency polygon to sick it the statistical
Deng
2.draw a histogram and frequency polygon to dipict the statistical table
Icecool
Describe the organizational setup of bureau of statics government of sindh give its past achievement in brief
Awais Reply
Life Table and its construction
Awais
only asking what is hospital statistics
Suly Reply
What's the meaning Of statistic
Farouk Reply
what's the meaning of statistic
Musa
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
khama Reply
pls I want to know the characterize of mean
Trixie Reply
I want solution to; x,x+1,3.5,3.4 and 2.5 is 3.1. find the value of x
Trixie
mean is nothing but average.
NAMDEV
(x+x+1+3.5+3.4+2.5)/5=3.1 2x+10.4=3.1*5 x=(15.5-10.4)/2 x=2.55
NAMDEV
How. Pls explain or break it down thanks
Icecool
the sum of all five divided by the 5 which is the average is equal to 3.1 so you sum them, divide and equate to 3.1. then solve for X by making X the subject
Pascale
Think of it as your grade, or gpa. how do you find the average of it?
La
great
Rushikesh
nicely explained
Rushikesh
What is the meaning of statistics and it's relevance in the social sciences
Icecool Reply
statistics is the branch of mathematics that using math& statistics theories to interpret data to information which is supporting the decision makers in social sciences and applied too. statistics is decision making science now aday
Ishag
I want to slove this math
Enny Reply
I'm not seeing the Math problem?
Debra
the data below where from 1 miles. miles 1:8380, 8210,3836,7840,7910,7510,7720,7750,8100,7690 test wherever their difference is significance at 5% level with population of #8000.
Enny
1*1
Enny
me too
New
enny i don't see any math problems
New
hello my friend. how can you help me to solve math
ott
help me the interquartile range and semi interquartile range of grouped data
Ishraaq
what is the difference between macro and micro data?
Sani Reply
Macrodata consist of 'headcounts', Microdata contain data on individuals,
Cherry
macro is a big business and micro is small business
Mukhtar
macro means whole or big and micro means part or small therefore in relation to data, macro data will be big or whole data and micro data will be small or individual part of a data. for example taking the whole data of an organisation or economy that will be macro data and taking the data on employe
Pascale
employees will be micro data
Pascale
How to determine appropriate statistics tool for my data
Jayr Reply
hi
Juliana
hi
Emy
You cannot know everything! Statistics is a vast subject so don’t be afraid to say that you don’t know. Ask others for help or look up information on the internet to help. Don’t assume that the student knows anything about the technique they are suggesting!
Kalu
well
Tahir
my class starts at February 4th
Elaine
P is the probability that a given die shows even number. To test H0 : P =1/2 against H1 : P=1/3, following procedure is adopted. Toss the die twice and accept H0 if both times it shows even number. Find the probabilities of type I and type II errors
Loyolite Reply
what is statistics?
bilal Reply
what is data
natnael
It Is the collection, collation,Analysing Interpretation,and presentation of data....
Tosayo
statistics is a science that studies numerical values assigned to objects, attributes or variables in order to characterize and make the variables more meaningful.
Okosa
statistics is the science of collection, analysis, Interpretation & presentation of numerical data
Kishan
Numeric data
Tosayo
if you think about normal number and operations of math such as fractions and percent values, statisitics is when it comes down to it a lot of just that - counting and then fractions, then that data and those counts (and ratios)/fractions that were used or counted in one group will represent a pop.
Jesus
An example is, lets say you are in charge of making large orders of supplies and that based on your need of X bricks = X feet of building - now thats the math, well stats is using that math in a way the next person making orders can base those orders of what they will need based on saying "in this
Jesus
..case, when Bilal needed 75 feet of building walls that 150 bricks were used" - now, that helps to get one job done but if we then watch those jobs one at a time, and count that 5/5 times the count was 150 bricks total - the new person could order 150 bricks with a high probability of being right
Jesus
If X is a Uniform random variable in [ -2, 2 ], find the pdf of Y X  and E Y[ ].
Kezang Reply
could you resend the question it is not clear after " the PDF of---" ?
Anji
ap kis year ki student ho
Shahjee
Mastrs ist year
Anaya
I'm from 2nd year BHU
abhishek
ap kis year ki student ho
Shahjee
I'm student of bs(hons) 1st year
bilal
tell me good definition of statistics?
bilal
Practice Key Terms 2

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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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