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The document introduces statistical hypothesis testing. It defines the null and alternative hypotheses, and explains that tests can be left-tailed, right-tailed, or two-tailed depending on the alternative hypothesis. The summary statistics and p-value are used to either reject or fail to reject the null hypothesis. Type I and II errors are explained. An example hypothesis test is provided to illustrate the process.

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AP/H Statistics Mrs. LeBlanc Perrone Name: ______________________________ Date: ___________ 8.1 Guided Notes 8.1 INTRODUCTION TO STATISTICAL TESTS In this chapter, we will focus on ________________________________________________________________ __________________________________________________________________________________________ Stating Hypotheses o Two Types of Hypotheses NULL HYPOTHESIS - ALTERNATE HYPOTHESIS - _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ SYMBOLS: SYMBOLS: o Example 1: Null and Alternate Hypotheses A car manufacturer advertises that its new subcompact models get 47 miles per gallon (mpg). Let be the mean of the mileage distribution for these cars. You assume that the manufacturer will not underrate the car, but you suspect that the mileage might be overrated. State the null and alternate hypotheses. 1
AP/H Statistics Mrs. LeBlanc Perrone Types of Tests We categorize a statistical test according to the _____________________________ Null Hypothesis Alternate Hypothesis and Type of Test Left-Tailed Test Right-Tailed Test Two-Tailed Test Important Vocabulary For Hypothesis Tests o Sample Test Statistic: ____________________________________________________________ ______________________________________________________________________________ Basic Process of Hypothesis Tests 1. ______________________________________________________________________________ ______________________________________________________________________________ 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ 4. ______________________________________________________________________________ 5. ______________________________________________________________________________ 2
AP/H Statistics Mrs. LeBlanc Perrone P-Value o Assuming is true, the P-value of the test is ________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ o P-value and Types of Tests Let represent the standardized sample test statistic for testing a mean using the standard normal distribution. Left-Tailed Test Right-Tailed Test Two-Tailed Test 3
AP/H Statistics Mrs. LeBlanc Perrone Types of Errors o Type I Error: __________________________________________________________________ ______________________________________________________________________________ o Type II Error: __________________________________________________________________ ______________________________________________________________________________ o Type I and Type II Errors Our Decision Truth of And if we do not reject And if we reject o Level of Significance: ____________________________________________________________ ______________________________________________________________________________ Symbol: _____ o Beta: _______________________________________________________________________ The probability of a type II error is treated in advanced statistics courses, we will focus on the probability of a type I error. o Summary of the probabilities or errors associated with a statistical test Our Decision Truth of And if we do not reject And if we reject 4
AP/H Statistics Mrs. LeBlanc Perrone Concluding a Statistical Test o is specified in advance before any samples are drawn o Compare with the P-value If P-value , ___________________________________________________________ ________________________________________________________________________ If P-value > , ____________________________________________________________ ________________________________________________________________________ o When we accept or fail to reject , we need to understand that we are not proving . We are only saying that the sample evidence (data) is not strong enough to justify rejection of the null hypothesis. Meaning of the terms Fail to Reject and Reject Term Meaning o When cannot be rejected, a confidence interval us often used to estimate the parameter in question because it gives the statistician a range of possible values for the parameter. 5
AP/H Statistics Mrs. LeBlanc Perrone Example 2: Statistical Testing Preview Rosie is an aging sheep dog in Montana who gets regular checkups from her owner, the local veterinarian. Let be a random variable that represents Rosies resting heart rate (in beats per minute). From past experience, the vet knows that has a normal distribution with . The vet checked the Merck Veterinary Manual and found for dogs of this breed beats per minute. Over the past six weeks, Rosies heart rate (beats/min) measured: 93, 109, 110, 89, 112, 117. The sample mean is . The vet is concerned that Rosies heart rate may be slowing. Do the data indicate that this is the case? Use 6
AP/H Statistics Mrs. LeBlanc Perrone Summary Questions 1. Compare and Contrast Type I and Type II errors ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. In a statistical test we have a choice of a left-tailed test, right-tailed test, or two-tailed test, how do you decide which type of test to use? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. How do you decide the conclusion of a hypothesis test? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 4. If we fail to reject the null hypothesis, does this mean that we have proved it to be true beyond all doubt? Explain. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 7

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8.1 guided notes

  • 1. AP/H Statistics Mrs. LeBlanc Perrone Name: ______________________________ Date: ___________ 8.1 Guided Notes 8.1 INTRODUCTION TO STATISTICAL TESTS In this chapter, we will focus on ________________________________________________________________ __________________________________________________________________________________________ Stating Hypotheses o Two Types of Hypotheses NULL HYPOTHESIS - ALTERNATE HYPOTHESIS - _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ SYMBOLS: SYMBOLS: o Example 1: Null and Alternate Hypotheses A car manufacturer advertises that its new subcompact models get 47 miles per gallon (mpg). Let be the mean of the mileage distribution for these cars. You assume that the manufacturer will not underrate the car, but you suspect that the mileage might be overrated. State the null and alternate hypotheses. 1
  • 2. AP/H Statistics Mrs. LeBlanc Perrone Types of Tests We categorize a statistical test according to the _____________________________ Null Hypothesis Alternate Hypothesis and Type of Test Left-Tailed Test Right-Tailed Test Two-Tailed Test Important Vocabulary For Hypothesis Tests o Sample Test Statistic: ____________________________________________________________ ______________________________________________________________________________ Basic Process of Hypothesis Tests 1. ______________________________________________________________________________ ______________________________________________________________________________ 2. ______________________________________________________________________________ ______________________________________________________________________________ 3. ______________________________________________________________________________ ______________________________________________________________________________ 4. ______________________________________________________________________________ 5. ______________________________________________________________________________ 2
  • 3. AP/H Statistics Mrs. LeBlanc Perrone P-Value o Assuming is true, the P-value of the test is ________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ o P-value and Types of Tests Let represent the standardized sample test statistic for testing a mean using the standard normal distribution. Left-Tailed Test Right-Tailed Test Two-Tailed Test 3
  • 4. AP/H Statistics Mrs. LeBlanc Perrone Types of Errors o Type I Error: __________________________________________________________________ ______________________________________________________________________________ o Type II Error: __________________________________________________________________ ______________________________________________________________________________ o Type I and Type II Errors Our Decision Truth of And if we do not reject And if we reject o Level of Significance: ____________________________________________________________ ______________________________________________________________________________ Symbol: _____ o Beta: _______________________________________________________________________ The probability of a type II error is treated in advanced statistics courses, we will focus on the probability of a type I error. o Summary of the probabilities or errors associated with a statistical test Our Decision Truth of And if we do not reject And if we reject 4
  • 5. AP/H Statistics Mrs. LeBlanc Perrone Concluding a Statistical Test o is specified in advance before any samples are drawn o Compare with the P-value If P-value , ___________________________________________________________ ________________________________________________________________________ If P-value > , ____________________________________________________________ ________________________________________________________________________ o When we accept or fail to reject , we need to understand that we are not proving . We are only saying that the sample evidence (data) is not strong enough to justify rejection of the null hypothesis. Meaning of the terms Fail to Reject and Reject Term Meaning o When cannot be rejected, a confidence interval us often used to estimate the parameter in question because it gives the statistician a range of possible values for the parameter. 5
  • 6. AP/H Statistics Mrs. LeBlanc Perrone Example 2: Statistical Testing Preview Rosie is an aging sheep dog in Montana who gets regular checkups from her owner, the local veterinarian. Let be a random variable that represents Rosies resting heart rate (in beats per minute). From past experience, the vet knows that has a normal distribution with . The vet checked the Merck Veterinary Manual and found for dogs of this breed beats per minute. Over the past six weeks, Rosies heart rate (beats/min) measured: 93, 109, 110, 89, 112, 117. The sample mean is . The vet is concerned that Rosies heart rate may be slowing. Do the data indicate that this is the case? Use 6
  • 7. AP/H Statistics Mrs. LeBlanc Perrone Summary Questions 1. Compare and Contrast Type I and Type II errors ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. In a statistical test we have a choice of a left-tailed test, right-tailed test, or two-tailed test, how do you decide which type of test to use? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. How do you decide the conclusion of a hypothesis test? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 4. If we fail to reject the null hypothesis, does this mean that we have proved it to be true beyond all doubt? Explain. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 7