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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

mean is number that occurs frequently in a giving data
Chinedu Reply
That places the mode and the mean as the same thing. I'd define the mean as the ratio of the total sum of variables to the variable count, and it assigns the variables a similar value across the board.
Samsicker
what is mean
John Reply
what is normal distribution
RAHAT Reply
What is the uses of sample in real life
Waqas Reply
pain scales in hospital
Lisa
change of origin and scale
RAHAT Reply
3. If the grades of 40000 students in a course at the Hashemite University are distributed according to N(60,400) Then the number of students with grades less than 75 =*
Ahmad Reply
If a constant value is added to every observation of data, then arithmetic mean is obtained by
Madiha Reply
sum of AM+Constnt
Fazal
data can be defined as numbers in context. suppose you are given the following set of numbers 18,22,22,20,19,21
Tyasia Reply
what are data
Tyasia Reply
what is mode?
Natasha Reply
what is statistics
Natasha
statistics is a combination of collect data summraize data analyiz data and interprete data
Ali
what is mode
Natasha
what is statistics
Alex Reply
It is the science of analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.
Bernice
history of statistics
Terseer Reply
statistics was first used by?
Terseer
if a population has a prevalence of Hypertension 5%, what is the probability of 4 people having hypertension from 8 randomly selected individuals?
John Reply
Carpet land sales persons average 8000 per weekend sales Steve qantas the firm's vice president proposes a compensation plan with new selling incentives Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per sales
lorenda Reply
Supposed we have Standard deviation 1.56, mean 6.36, sample size 25 and Z-score 1.96 at 95% confidence level, what is the confidence interval?
John Reply

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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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