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Hypothesis Testing

⇒Identify the null hypothesis from a given claim, and express both in symbolic form

⇒Calculate the value of the test statistic, given a claim and sample data

⇒ Choose the sampling distribution that is relevant

⇒Either find the P-value or identify the critical values

⇒State the conclusion about a claim in simple and nontechnical terms

Part 1-Basic Concepts of Hypothesis Testing

In statistics a hypothesis claim or statement about a property of a population

XSORT Method

If the probability of getting a girl is 58/100 then the x sort method says p>0.5

Rare event rule for Inferential Statistics

If, under a given assumption the probability of a particular observed event is extremely small, we

conclude that the assumption is probably not correct.

Null Hypothesis

Statements that the value of a population parameter such as proportion, mean, or standard deviation)

is equal to some claimed value. ( the term null is used to indicate no change or no effect or no

difference). We test the null hypothesis directly in the sense that we assume or pretend it is true and

reach a conclusion to either reject or fail to reject it. Ho:p=0.5

Alternative Hypothesis

Statement that the parameter has a value that somehow differs from the null hypothesis. For the

methods of this chapter, the symbolic form of the alternative hypothesis must use one of these symbols:

<,>,≠

H1: p>0.5 H1: P<0.5 H1: P≠0.5

The original claim could become the null hypothesis in a claim that p=0.5, it could become the alternative

hypothesis ( as in the claim that p>0.5), or it might not be either the null hypothesis or the alternative

hypothesis (as in the claim that p ≥0.5)

P Value Method

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⇒1. Identify the specific claim or hypothesis to be tested and put in symbolic form

⇒2.Give the symbolic form that must be true when the original claim is false

⇒3. Of the two symbolic expressions obtained so far, let the alternative hypothesis H1 be the one

not, containing equality, so that H1 uses the symbol > or < or ≠

⇒4. Select the significance level a based on the seriousness of a type 1 error. Make a small if the

consequences of rejected a true Ho are severe. The values of 0.05 and 0.01 are very common

⇒5.Identify the statistic that is relevant to this test and determine its sampling distribution

⇒6. Find the test statistic and find the p value. Draw a graph and show the test statistic and p

value

⇒7.Reject H0 if the p value is less than or equal to the significance level a. Fail to reject HO if the

p value is greater than A.

⇒8.Restate this previous decision in simple,non technical terms, and address the original claim

Critical Value Method

⇒1. Identify the specific claim or hypothesis to be tested, and put it in symbolic form

⇒2. Give the symbolic form that must be true when the original claim is false

⇒3. Of the two symbolic expressions obtained so far, let the alternative hypothesis H1 uses the

symbol > or < or ≠. Let the null hypothesis be the symbolic expression that the parameter

equals the fixed value being considered

⇒4.Select the significance level A based on the seriousness of a type 1 error. Make A small if the

consequences of rejecting a true Ho are severe. The values of 0.05 and 0.01 are very common

⇒5. Identify the statistic that is relevant to this test and determine its sampling distribution ( such

as normal,t, chi square)

⇒6. Find the test statistic , the critical values, and the critical region. Draw a graph and include

the test statistic, critical values and critical region

⇒7. Reject Ho if the test statistic is in the critical region. Fail to reject Ho if the test statistic is not

in the critical region

⇒8. Restate this previous decision in simple, nontechnical terms and address the original claim.

Step 1: Identify the claim to be tested and express it in symbolic form. The proportion of girls is greater than

the proportion of 0.5 that occurs without any treatement.

Step 2. Give the symbolic form that must be true when the original claim is false. If the original claim of

p>0.5 is false, then P ≤ 0.5 must be true.

Step 3: This step is in two parts: Identify the alternative hypothesis H1 and identify the null hypothesis Ho.

Identify H1: Using the two sympoblic expressions P>0.5 and P ≤ 0., the alternative hypothesis H1 is the one

that does not contain equality. Of these two expressions, P>0.5 does not contain equality so we get

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