Formulation of hypothesis
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Transcript of Formulation of hypothesis
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FORMULATION OF HYPOTHESIS
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FORMULATING HYPOTHESIS
Begins with an assumption called HYPOTHESIS
HYPOTHESIS:An hypothesis is really a temporary
explanation, a kind of educated guess about what will happen under certain conditions.
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EXAMPLE
Q: Do plants need light to grow ?Ex: IF green plants need light to grow,
THEN only plants kept in light will display growth.
NOTE: Most of the times it is an “IF…. THEN… statement”
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Take the following and make an hypothesis
• Do living things give off CO2 when they digest food?
• A scientist think that living things give off carbon dioxide as they break down food. He predicts that carbon dioxide can be detected as an organism digests food.
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What is Hypothesis Testing
A set of logical and statistical guidelines used to make decisions from sample statistics to population characteristics.
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Hypotheses Testing
The intent of hypothesis testing is to formally examine two opposing conjectures (hypotheses), H0 and HA/H1
These two hypotheses are mutually exclusive and exhaustive.
Sample information is collected and analysed.
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Basic Concepts in Hypotheses Testing
• Null Hypotheses &Alternate Hypotheses• Level of Significance• Critical Region• Decision Rule(Test of Hypothesis)• Type I & Type II Errors• Two Tailed & One Tailed Tests• One Sample & Two Sample Tests
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NULL HYPOTHESIS
• Specific statement about a population parameter made for the purposes of argument.
• It Is always about a population parameter, not about a sample statistic.
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Alternate Hypothesis
• Represents all other possible parameter values except that stated in the null hypothesis.
• Denoted by H1 / HA.
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Level of Significance
• The critical probability in choosing between the null & alternative hypotheses.
• The higher the significance level, the higher the probability of rejecting a null hypothesis when its true.
• Confidence level:A percentage or decimal value that tells how confident a researcher can be about being correct.
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Critical Region
• The Acceptance and Rejection region.
• If the value of mean falls within the rejection region, the null hypothesis is rejected.
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Decision Rule(Test of Hypothesis)
The rule according to which we accept or reject null hypothesis.
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Type I Error & Type II Error
• A Type I error is the mistake of rejecting the null hypothesis when it is true.
• α- Type I error.
• A Type II error is the mistake of failing to reject the null hypothesis when it is false.
• β- Type II error.
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Type I Error & Type II Error
Accept H0 Reject H0
Correct Decision Type I Error
Type II Error Correct Decision
Ho (True)
Ho (False)
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Type I Error & Type II Error
Suppose there is a test for a particular disease. • If the disease really exists and is diagnosed early, it
can be successfully treated• If it is not diagnosed and treated, the person will
become severely disabled• If a person is erroneously diagnosed as having the
disease and treated, no physical damage is done
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Type I Error & Type II Error
Decision No disease Disease
Not diagnosed OK
Type I error
Diagnosed Type II error
OK
treated but not harmed by the treatment
irreparable damage would be done
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One Tailed & Two Tailed Test
• Two-Tailed Tests
• If the null hypothesis is rejected for values of the test statistic falling into either tail of its sampling distribution.
• A deviation in either direction would reject the null hypothesis
• Normally α is divided into α/2 on one side and α/2 on the other.
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One Tailed & Two Tailed Test
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One Tailed & Two Tailed Test
• One-Tailed Tests
• Only used when the other tail is nonsensical.
• If null hypothesis is rejected only for values of the test statistic falling into one specified tail of its sampling distribution.
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One Tailed & Two Tailed Test
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One Tailed & Two Tailed Test
• A manufacturer of a light bulb wants to produce bulbs with a mean life of 1000 hours. If the lifetime is shorter, he will lose customers to the competitors; if the lifetime is longer, he will have a very high production cost because the filaments will be very thick. Determine the type of test.
The wholesaler buys bulbs in large lots & does not want to accept bulbs unless their mean life is at least 1000 hours. Determine the type of test.
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One Sample & Two Sample Tests
• One Sample TestWhen we want to draw inferences about the population on the basis of given sample.
• Two Sample TestWhen we want to compare and draw inferences about 2 populations on the basis of given samples.
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Independent & Paired Samples
• Independent SamplesDrawn randomly from different populations.
• Paired SamplesWhen the data for the two samples relate to the same group of respondents.
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Types of Hypotheses
• Research hypotheses.
• Logical hypotheses.– Null hypothesis (Ho).– Alternative hypothesis (HA/H1).
• Statistical hypotheses.