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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

what percent of the students would be expected to score above 95?
Peachy Reply
inferential statistics is what?
Seyi Reply
in which we make infrences (hypothsis)
asad
surpose a data set of 2,3,5,6,1,4 are given find median
lucy Reply
fastest finger please
lucy
Mean (average) 4... Median (middle term) 3.5.. Mode (frequency) every element in a set has 1 frequrncy
Akash
i arrange the data set in ascending order. that is, 1,2,3,4,5,6. then find the data set that falls in the middle. in this case, 3 & 4 fall in the middle. you then sum and obtain the average. that is, (3+4)/2=3.5. therefore, 3.5 is the median.
Gbenga
both of you are correct.
Joseph
hello guys
Abasikponke
thanks
lucy
great to be here
King
how does a line graph look
King
hi
Davia
hello
lucy
pls who knows how line graph look like
King
line graph usually have a straight line running through axis
Dike
am new here anyone willing to orient me?
Timothy
find the media of the following numbers 61,64,67,70,73
lucy Reply
my body pls
lucy
67
Benmike
what happen to your body@hana
Benmike
what is the percentile for the set of data in the class C and frequency F(c,f)given by (9.3-9.7,2) (9.8-10.2,5) (10.3-10.7,12) (10.8-11.2,17) (11.3-11.7,14) (11.8-12.2,6) (12.3-12.7,3) (12.8-13.2,1)
Chinwendu Reply
how to find median
Hrishe Reply
arrange ascending and desending order than the mid value is Median
rajendra
ok
Hrishe
what if it is a group data
Oloyede
mean/ medium/ mode
Michelle
n\2 and n+1\2
asad
An operational manager at a manufacturing company is interested in the level of satisfaction of computer buyers. The manager has developed a satisfaction scale of 1-10 to mark their level of understanding with the company.What is the population of the interest?
thomas Reply
Any clues
Virtual
how to use grouped and ungrouped data
Hassan Reply
Just a test from gplay
Lucy Reply
how come 5.67
Mano Reply
by dividing 11.37 on 2
saifuddin
by dividing 11.34 on 2
saifuddin
what is index number?
vinayak
What is the differences between quota an lottery system of sampling
EGBE
What are the are the characteristics that are critically expedients in selecting the sample size
EGBE
fit a binomial distribution for the following data and test the goodness of fit x: 0 1 2 3 4 5 6 f: 5 18 28 12 7 6 4
Mikki Reply
solution
Mano
solve the question please
Mano
can some please help solve so that we learn some
Simonsakala
It is a square chi
Nelson
But can't be a binomial because, the x numbers are 0 to 6, instead those would be "0" or "1" in a straight way
Nelson
You can do a chi-square test, but the assumption has to be a normal distribution, and the last f's number need to be "64"
Nelson
sorry the last f's numbers : "6 and 4" which are the observed values for 5 and 6 (expected values)
Nelson
hi
rajendra
can't understand basic of statistics ..
rajendra
Sorry I see my mistake, we have to calculate the expected values
Nelson
So we need this equation: P= (X=x)=(n to x) p^x(1-p)^n-x
Nelson
why it is not possible brother
ibrar
were n= 2 ( binomial) x= number of makes (0 to 6) and p= probability, could be 0.8.
Nelson
so after we calculate the expected values for each observed value (f) we do the chi-square. x^2=summatory(observed-expected)^2 / expected and compare with x^2 in table with 0.8
Nelson
tomorrow I'll post the answer, I'm so tired today, sorry for my mistake in the first messages.
Nelson
It is possible, sorry for my mistake
Nelson
two trader shared investment and buoght Cattle.Mr.Omer bought 255 cows & rented the farm for a period of 32 days. Mr. Ahmed grazed his Cattle for 25 days. Mr. Ahmed's cattle was 180 cows.Together they profited $ 7800. the rent of the farm is $ 3000 so divide the profit per gows/day for grazing day
Mohamed
how to start this book, who is reading thins first time
Nissar Reply
It is my first time reading this book
Qader
Good one
ihsan
from were did you get 2/50?m
Chico Reply
People living longer
Qader Reply
Why do you think that is?
Jazzy
because there is an increase in number of people with age more than 30.
Qader
Ok. And what do you think is the driving factor behind that hypothesis?
Jazzy
fewer birth and increase in # of years living or fewer dying
Qader
What about the improvement of technology and medicine?
Jazzy
please help me, with this.... three coins are tossed let be the number of head(h)obtain,construct a probability distribution for X
godwin
technology and medicine is improving but they are limited
Ayunku
If those conscience of their health, one will live longer periods of life.
Montrae
hi,why the mean =sum(xi)/n but the variance =sum(xi-xbar)/ n-1 what is the difference between (n or n-1)
Soran Reply
This is hard to type, so I'll use "m" for "x bar", and a few other notations that I hope will be clear: Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n Desired formula: sqrt((SUM[x^2] - SUM[x]^2)/n / (n-1)) Now let's do what you started to do, and see if we can manipulate the definitio
Michael
what is the difference between (n ) and (n-1) in the mean and variance
Soran
Definition: sqrt(SUM[(x - m)^2] / (n-1)) where m = SUM[x] / n what is the difference between (n and n-1)
Soran
Hi, the diference is tha when we estimate parameters in a sample (not in the total population) we need to consider the degrees of liberty for the estimation.
Nelson
Hie guys, am analysing rainfall data for different stations and i got kurtosis values of 0.7 for one station and 0.4 for another, what can i say about this?
Kudakwashe
hi
ujjal
difference in degrees of freedom
vinayak

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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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