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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

frequency distribution table
Ali Reply
sum of dots when 2 dice are rolled is
Babra Reply
what is statistics?
Noman Reply
Statistics is the collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.
John
you are right
razia
you are right
razia
a random variable is __________ if takes on a values continuous scale.
Loida Reply
merits of arithmetic mean
Priya Reply
formula of HM
Bikram
hello
umar
hi
Candyda
n/sum(1/xi). this i is in subscript
moniba
this is HM formula
moniba
Thank you
Candyda
So guys u can help me get better in statistics
Lion
class interval and class limit are same ?
Shantal Reply
what is a differnece between class interval and class boundries ?
Shantal
I don't think so
Plain
interval between the element of class- class interval
Hemanta
class boundary consist of the upper and lower class limits but class class limit is the same decimal values as the data values
Najeeb
x 0 1 2 3 4 5 0.05 0.09 0.17 0.27 0.23 0.19 a) Find the probability that 1 or 2 smart phones have defects (show calculations). b) Find the probability that more than 3 smart phones have defects (show calculations). c) Find the probability that at most 2 smart phones have defects (show calculat
Mr Reply
Please expand on the number set data
Jesus
what is proportion?
Ann Reply
A proportion is simply a statement that two ratios are equal
Foeor
Two dice are thrown. Let A be the event that the sum of the upper face number is odd and be the event of at least one ace
Sana Reply
does proportion alwaus give u a yes or no answer for data
Adrienne Reply
frequency destribution
the Reply
7.The following data give thenumber of car thefts that occurred in a city in the past 12 days. 63711438726915 Calculate therange, variance, and standard deviation.
Mitu Reply
express the confidence interval 81.4% ~8.5% in interval form
Xx Reply
a bad contain 3 red and 5 black balls another 4 red and 7 black balls, A ball is drawn from a bag selected at random, Find the probability that A is red?
Shazain Reply
The information is given as, 30% of customers shopping at SHOPNO will switch to DAILY SHOPPING every month on the other hand 40% of customers shopping at DAILY SHOPPING will switch to other every month. What is the probability that customers will switch from A to B for next two months?
sharmin Reply
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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