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Determine both Type I and Type II errors for the following scenario:

Assume a null hypothesis, H 0 , that states the percentage of adults with jobs is at least 88%.

Identify the Type I and Type II errors from these four statements.

  1. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%
  2. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.
  3. Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.
  4. Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%.

Type I error: c

Type I error: b

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Chapter review

In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected.

The probabilities of these errors are denoted by the Greek letters α and β , for a Type I and a Type II error respectively. The power of the test, 1 – β , quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.

Formula review

α = probability of a Type I error = P (Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

β = probability of a Type II error = P (Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

Type I: The mean price of mid-sized cars is $32,000, but we conclude that it is not $32,000.

Type II: The mean price of mid-sized cars is not $32,000, but we conclude that it is $32,000.

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A sleeping bag is tested to withstand temperatures of –15 °F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

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For Exercise 9.12 , what are α and β in words?

α = the probability that you think the bag cannot withstand -15 degrees F, when in fact it can

β = the probability that you think the bag can withstand -15 degrees F, when in fact it cannot

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In words, describe 1 – β For Exercise 9.12 .

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A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H 0 , is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.

Type I: The procedure will go well, but the doctors think it will not.

Type II: The procedure will not go well, but the doctors think it will.

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A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H 0 , is: the surgical procedure will go well. Which is the error with the greater consequence?

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The power of a test is 0.981. What is the probability of a Type II error?

0.019

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A group of divers is exploring an old sunken ship. Suppose the null hypothesis, H 0 , is: the sunken ship does not contain buried treasure. State the Type I and Type II errors in complete sentences.

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A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H 0 , is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?

0.998

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A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H 0 , is: the sample contains E-coli. Which is the error with the greater consequence?

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Questions & Answers

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
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
I want to know statistics
Okosa Reply
why is data so important in statistics
Trixie Reply
want summary statistic on gender, age group, weight, and weight loss
Trixie
are you asking question or looking for Solution
Arun
solution pls
Trixie
1st convert gender and group to factor than use summary function It will give mean median and mode with other details
Arun
its a bit complicated could u bring it to my level of under standing
Trixie
u know the question was put in a tabular form where we were to find the variable type, summary statistics and graph type of the given variables that's the gender,age group, weight and weight loss
Trixie
if you see, gender and group are not numerical due to which they will not give you correct statistics
Arun
how you denote gender m or f
Arun
or t
Arun
ok tnk u
Trixie
these are not numerical so you have to convert they as f=1; m=2; t=3 same thing you have to do with group or any variable which is character else you should drop them
Arun
from your calculation
Arun
oh OK tnk u
Trixie
so pls why is data important in statistics
Trixie
not only data correct data is imp
Arun
statistics works on data only
Arun
without data you can not summarize, can not predict future, can not establish relationship between two and more variables, can not prepare reports and make decisions on it
Arun
so I'll give example. suppose you want to open a restaurant and you have to choose one best location out of 5. then how you will decide which location is best for you
Arun
awww thank you pls
Trixie
pls I want a brief note on observation, survey and experimentation way of obtaining data
Trixie
hi
Abdiwahab
please Tell me difference parameters and non parameter
Abdiwahab
can you tell me about the scopes of statistics?
Minhal
plzzz answer me anyone .
Minhal
Methods of Collecting Data Observation Observational studies allow researchers to document behavior in a natural setting and witness events that could not be produced in a lab.
Arun
Key Points Observation differs from most other forms of data collection in that the researcher does not manipulate variables or directly question participants. The advantages of observation include observing natural behavior, refining hypotheses, and allowing for observation of behavior that canno
Arun
 be produced in an artificial environment for ethical or practical reasons. The disadvantages of observation are that these studies do not produce quantitative data, do not allow for cause and effect statements, may be very time consuming, and can be prone to researcher bias.
Arun
Key Terms observational research: Research focusing on the observation of behavior outside of a laboratory setting. external validity: In research, whether or not study findings can be generalized to real world scenarios.
Arun
Surveys and Interviews Surveys are a low-cost option for gathering a large amount of data, but they are also susceptible to reporting bias.
Arun
Key Points The survey method of data collection is likely the most common of the four major research methods. The benefits of this method include low cost, large sample size, and efficiency.
Arun
The major problem with this method is accuracy: since surveys depend on subjects’ motivation, honesty, memory, and ability to respond, they are very susceptible to bias. A researcher must have a strong understanding of how to properly frame survey questions in order to gather reliable and relevant
Arun
Key Terms reliability: The degree to which a measure is likely to yield consistent results each time it is used. validity: The degree to which a measure is actually assessing the concept it was designed to measure. survey: A method for collecting qualitative and quantitative information about ind
Arun
individuals in a population.
Arun
Interviews Interviews are a type of qualitative data in which the researcher asks questions to elicit facts or statements from the interviewee. Interviews used for research can take several forms:
Arun
Informal Interview: A more conversational type of interview, no questions are asked and the interviewee is allowed to talk freely. General interview guide approach: Ensures that the same general areas of information are collected from each interviewee. Provides more focus than the conversational ap
Arun
approach, but still allows a degree of freedom and adaptability in getting the information from the interviewee. Standardized, open-ended interview: The same open-ended questions are asked to all interviewees. This approach facilitates faster interviews that can be more easily analyzed and compared
Arun
Closed, fixed-response interview (Structured): All interviewees are asked the same questions and asked to choose answers from among the same set of alternatives.
Arun
experiments An experiment involves the creation of a contrived situation in order that the researcher can manipulate one or more variables whilst controlling all of the others and measuring the resultant effects.
Arun
Boyd and Westfall1 have defined experimentation as: "...that research process in which one or more variables are manipulated under conditions which permit the collection of data which show the effects, if any, in unconfused fashion."
Arun
Experiments can be conducted either in the field or in a laboratory setting. When operating within a laboratory environment, the researcher has direct control over most, if not all, of the variables that could impact upon the outcome of the experiment
Arun
When experiments are conducted within a natural setting then they are termed field experiments. The variety test carried out by United Fruits on their Gros Michel and Valery bananas is an example of a field experiment.
Arun
parameter Parameters are factors or limits which affect the way that something can be done or made
Arun
Minhal didny get your question, can you please elaborate more
Arun
pls can u use mean n mode at the statistical summary pls
Trixie
yes, statistical summary itself gives all value
Arun
but u didn't tell me the advantage and disadvantage of the experimental method
Trixie
but you didn't tell me the advantage and disadvantage of experimental method
Trixie
tell me to make a hosrogram of dicrete values
Husnain
histogram
Husnain
noted!
Abdullahi
by using a sampling distribution? how to estimate the population mean using a ramdom variable n?
Jade Reply
what is the important of statistics
Shamsuddeen

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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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