HYPOTHESES Testing

HYPOTHESES Testing - TEST OF HYPOTHESIS TEST OF HYPOTHESIS...

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Unformatted text preview: TEST OF HYPOTHESIS TEST OF HYPOTHESIS There are many problems in which, rather then estimating the value of a parameter, we need to decide whether to accept or reject statement about the parameter. This statement is called hypothesis and the decision making procedure about the hypothesis is called Hypothesis-Testing. For e.g. a) The teaching method in both the institutes are effective b) The average IQ of normal human being is 113 Statistical Hypotheses A verbal statement or claim ,about a population parameter is called a Statistical Hypotheses To Test a population Parameter we state a pair of Hypotheses:- a) NULL HYPOTHESES b) ALTERNATE HYPOTHESES CONTD.. . , , ≥ = ≤ Null Hypotheses H :- It is a statistical hypotheses that contains a statement of Equality such as :- Alternate Hypotheses H 1 :- It is the complement of the null hypotheses. It is a statement that must be true if H0 is false and it contains a statement of inequality ,such as >,< or ≠ = ≤ ≥ o r , CONTD.. k H k H g e k H k H g e ≠ = < ≥ μ μ μ μ : ... .......... : ...... 2 . : ... .......... : ....... 1 . 1 1 PROBLEM1 ( Stating the Null and Alternate Hypotheses ) Write the claim as a mathematical sentence .State the null and alternate hypotheses, and identify which represents the claim. a) A university publicizes that proportion of its students who graduate in 4 years is 82%. b)A cereal company advertises that the mean weight of the contents of its 20 –ounce size cereal boxes is more than 20 ounces. Solution a) The claim ‘the proportion….82%’ can be written as p = 0.82 contains the statement of equality ,it becomes the null hypotheses. H : p = 0.82(claim) H 1 : p≠ 0.82 bThe claim ‘the mean……..than 20 ounces’can be written as µ > 20.Its complement is µ 20. because µ 20. contains the statement of equality it becomes null hypotheses ≤ ≤ Thus ) ( 20 : 20 : 1 claim ounces H ounces H ≤ μ μ Note:- When we perform a hypotheses testing we make one of the two decisions: i) Reject the null hypotheses or ii) Accept the null hypotheses since our decision is based on the sample rather than the entire population there is always possibility we will make wrong decision. TYPES OF ERROR AND LEVEL OF SIGNIFICANCE In testing a statistical hypotheses ,we will encounter Typical Situations These typical situations give rise to two types of error.. : Accept H Reject H H is true Correct decision Type I error H is false Type II error Correct decision i) Type I error :-we may reject a hypotheses H when H is true.. ii) Type II error :- we may accept a hypotheses when H is false . PROBLEM 2 (Identifying TypeI and TypeII error) The USDA limit for salmonella contamination for chicken is 20%. A meat inspector reports that the chicken produced by a company exceeds the USDA limit.You perform a hypotheses test to determine whether meat inspector’s claim is true.When will type I or type II error occur? Solution Let p represent the proportion of the chicken that is contaminated. The meat inspector’s claim is “more than 20%”contaminated....
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HYPOTHESES Testing - TEST OF HYPOTHESIS TEST OF HYPOTHESIS...

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