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8.3 p value

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1) Testing a proportion uses a binomial distribution with hypotheses about p, the probability of success on each trial. The test statistic is calculated and compared to a normal distribution to get a p-value. 2) An example tests whether a new eye surgery technique is better than the old technique based on a trial with 225 surgeries and 88 successes, using a 1% significance level. 3) Key steps are to check conditions, calculate the test statistic, find the p-value using the normal distribution, and either reject or fail to reject the null hypothesis based on the significance level.

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AP/H Statistics Mrs. LeBlanc Perrone Name: ______________________________ 8.3: P-ValueGuided Notes Date: ___________ 8.3 TESTING A PROPORTION (P-VALUES) Testing a Proportion o Throughout this section we will assume that the situations we are dealing with satisfy the conditions of a binomial distribution _____ is the number of successes out of trials is the estimate for , the _____________________________________________ on each trial represents the _______________________________ on each trial The samples are large: and For large samples, the distribution is ____________________________________________________________________with and Hypotheses for Testing Left Tailed Test :___________ Note: :___________ The P-Value is the total areain the shaded region, bounded by the test Right Tailed Test statistic :___________ :___________ Two Tailed Test :___________ :___________ 1
AP/H Statistics Mrs. LeBlanc Perrone How to Test 1. ______________________________________________________________________________ Is this a binomial experiment with trials? Does represent the probability of success? Identify Is the sample large? (Is and ?) (Use p from ) If yes, then the distribution can be approximated by the normal distribution 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ Sample Test Statistic: 4. ____________________________________________________________________________ ______________________________________________________________________________ use the standard normal distribution 5. ______________________________________________________________________________ If P-value , we reject If P-value > , we fail to reject 6. ______________________________________________________________________________ 2
AP/H Statistics Mrs. LeBlanc Perrone o Example: Testing A team of eye surgeons has developed a new technique for a risky eye operation to restore the sight of people blinded from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight. Suppose that surgeons in various hospitals have performed a total of 225 operations using the new method and that 88 have been successful (i.e., the patients fully recovered their sight). Can we justify the claim that the new method is better than the old one? (Use a 1% level of significance.) 3
AP/H Statistics Mrs. LeBlanc Perrone Summary Questions 1. How is testing (using P-values) similar to testing (using P-values)? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. How do you find the total area in each tail, when testing using P-values? (Choose one method: using the table or using the calculator. Hint: its a similar process to what we did in chapter 6) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. What does it mean to reject or fail to reject ? (Hint: see section 8.1) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 4

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8.3 p value

  • 1. AP/H Statistics Mrs. LeBlanc Perrone Name: ______________________________ 8.3: P-ValueGuided Notes Date: ___________ 8.3 TESTING A PROPORTION (P-VALUES) Testing a Proportion o Throughout this section we will assume that the situations we are dealing with satisfy the conditions of a binomial distribution _____ is the number of successes out of trials is the estimate for , the _____________________________________________ on each trial represents the _______________________________ on each trial The samples are large: and For large samples, the distribution is ____________________________________________________________________with and Hypotheses for Testing Left Tailed Test :___________ Note: :___________ The P-Value is the total areain the shaded region, bounded by the test Right Tailed Test statistic :___________ :___________ Two Tailed Test :___________ :___________ 1
  • 2. AP/H Statistics Mrs. LeBlanc Perrone How to Test 1. ______________________________________________________________________________ Is this a binomial experiment with trials? Does represent the probability of success? Identify Is the sample large? (Is and ?) (Use p from ) If yes, then the distribution can be approximated by the normal distribution 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ Sample Test Statistic: 4. ____________________________________________________________________________ ______________________________________________________________________________ use the standard normal distribution 5. ______________________________________________________________________________ If P-value , we reject If P-value > , we fail to reject 6. ______________________________________________________________________________ 2
  • 3. AP/H Statistics Mrs. LeBlanc Perrone o Example: Testing A team of eye surgeons has developed a new technique for a risky eye operation to restore the sight of people blinded from a certain disease. Under the old method, it is known that only 30% of the patients who undergo this operation recover their eyesight. Suppose that surgeons in various hospitals have performed a total of 225 operations using the new method and that 88 have been successful (i.e., the patients fully recovered their sight). Can we justify the claim that the new method is better than the old one? (Use a 1% level of significance.) 3
  • 4. AP/H Statistics Mrs. LeBlanc Perrone Summary Questions 1. How is testing (using P-values) similar to testing (using P-values)? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. How do you find the total area in each tail, when testing using P-values? (Choose one method: using the table or using the calculator. Hint: its a similar process to what we did in chapter 6) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. What does it mean to reject or fail to reject ? (Hint: see section 8.1) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 4