Chapter 7 Notes 7-1: Hypotheses Null Hypothesis (H0)

Chapter 7 Notes 7-1: Hypotheses Null Hypothesis (H0)

Chapter 7 Notes 7-1: Hypotheses Null Hypothesis (H0) ALWAYS contains an element of equality (Either , , or =) Alternate Hypothesis (Ha) ALWAYS strictly inequality (Either <, >, ) The alternate hypothesis is the COMPLEMENT of the null hypothesis. If H0 is , then Ha is <. If Ha is <, it is called a left-tail test If H0 is , then Ha is >. If Ha is >, it is called a right-tail test If H0 is =, then Ha is . If Ha is , it is called a two-tail test Either one of these hypotheses may be the claim you have to read

the question/statement to determine which one represents the claim. We ALWAYS test the NULL hypothesis (Reject or Fail to Reject) Chapter 7 Notes 7-1: Hypotheses Types of Errors Type I Reject the null hypothesis when it was actually true (False negative) Type II Fail to reject the null hypothesis when it is false (False positive) Chapter 7 Notes 7-1: Hypotheses Level of Significance (- Greek letter Alpha) The maximum allowable probability of making a Type I error. This will be given to you.

If the null hypothesis is true, a P-value (or probability value) of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme as or more extreme than the one determined from the sample data. The area of P depends on the type of test and is determined by the . If the alternate hypothesis is less than, its a left-tail test. If the alternate hypothesis is greater than, its a right-tail test. If the alternate hypothesis is not equal to, its a two-tail test Chapter 7 Notes Hypotheses Steps for Hypothesis Testing 1) State the claim mathematically and verbally. Identify the null and alternate hypotheses. 2) Specify the level of significance (will be given to you). 3) Determine the standardized sampling distribution. 4) Calculate the test statistic and its standardized value.

5) Find the P-value. There MAY be a test that the calculator can run that will do steps 4 and 5 all at once. 6) Use the following decision rule: If the P-value is < the level of significance, reject . If the P-value is > the level of significance, fail to reject . 7) Write a statement to interpret the decision in the context of the original claim. Chapter 7 Notes Hypotheses Steps for Hypothesis Testing You can not use a hypothesis test to support your claim if your claim is the null hypothesis. If you want a conclusion that supports your claim, word your claim so

that it is the alternate hypothesis. If you want to reject a claim, word it so it is the null hypothesis. Chapter 7 Notes Hypotheses Example 1 (Page 366) Write the claim as a mathematical sentence. State the null and alternate hypotheses, and identify which represents the claim. Also, determine whether it is a left-tail, right-tail, or two-tail test. 1) A university publicizes that the proportion of its students who graduate in 4 years is 82%. The mathematical sentence is p = .82. Since this statement contains the statement of equality, it becomes the null hypothesis. The alternate hypothesis is p .82.

In this case the null hypothesis represents the claim. (Claim) This is a Two-Tailed test. Chapter 7 Notes Hypotheses Example 1 (Page 366) Write the claim as a mathematical sentence. State the null and alternate hypotheses, and identify which represents the claim. 2) A water faucet manufacturer announces that the mean flow rate of a certain type of faucet is less than 2.5 gallons per minute. < 2.5 There is no statement of equality in this sentence; it is the alternate hypothesis.

The complement of < 2.5 is 2.5, which becomes the null hypothesis. In this case the alternate hypothesis represents the claim. (Claim) This is a Left-Tailed test. Chapter 7 Notes Hypotheses Example 1 (Page 366) 3) A cereal company advertises that the mean weight of the contents of its 20-ounce size cereal is more than 20 ounces. > 20 There is no statement of equality in this sentence; it is the

alternate hypothesis. The complement of > 20 is 20, which becomes the null hypothesis. In this case the alternate hypothesis represents the claim. (Claim) This is a Right-Tailed test. Chapter 7 Notes Hypotheses Try these at your desk: Write the hypotheses and identify which one is the claim. A consumer analyst reports that the mean life of a certain type of automobile battery is not 74 months. (Claim) A television manufacturer publishes that the variance of the

life of a certain type of television is less than or equal to 3.5 years. (Claim) A radio station publicizes that its proportion of the local listening audience is greater than 39%. (Claim) Chapter 7 Notes Hypotheses Example 2 (Page 368) 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 hypothesis test to determine whether the meat inspectors claim is true. When will a Type I or Type II error

occur? Which is more serious? (Claim) A type I error will occur if the actual proportion of contaminated chicken is less than or equal to 0.2, but you decide to reject . (False negative) A type II error will occur if the actual proportion of contaminated chicken is greater than 0.20, but you do not reject (False positive) Which is more serious? Type II is more serious: A Type I error might create a health scare and hurt sales of chicken that was actually safe, but a Type II error allows the sale of contaminated chicken, possibly Chapter 7 Notes

Hypotheses Example 2 (Page 368) A company specializing in parachute assembly states that its main parachute failure rate is not more than 1%. You perform a hypothesis test to determine whether the companys claim is false. When will a type I or type II error occur? Which is more serious? (Claim) A type I error will occur if the actual failure rate of the main parachute is less than or equal to 0.01, but you decide to reject . (False negative) A type II error will occur if the actual failure rate of the main parachute is greater than 0.01, but you do not reject (False positive)

Which is more serious? Type II is more serious: Type I error might hurt sales of parachutes that were actually safe. Chapter 7 Notes Hypotheses Example 4 (Page 372) You perform a hypothesis test for each of the following claims. How should you interpret your decision if you reject ? If you fail to reject ? (Claim): A university publicizes that the proportion of its students who graduate in 4 years is 82%. The claim is the null hypothesis, so if you reject the null hypothesis, then you reject the claim. There is sufficient evidence to indicate that the

universitys claim is false. The claim is the null hypothesis, so if you fail to reject the null hypothesis, then you fail to reject the claim. There is NOT sufficient evidence to indicate that the universitys claim is false. Chapter 7 Notes Hypotheses Example 4 (Page 372) (Claim): Consumer Reports states that the mean stopping distance (on a dry surface) for a Honda Civic is less than 136 feet. The claim is the alternate hypothesis, so if you reject the null hypothesis, you support the claim. Remember, the is that the stopping distance is 136 feet.

The claim is the alternate hypothesis, so if you fail to reject the null hypothesis, you reject the claim. Chapter 7 Notes Hypotheses Example 5 (Page 374) A medical research team is investigating the benefits of a new surgical treatment. One of the claims is that the mean recovery time for patients after the new treatment is less than 96 hours. How would you write the null and alternate hypotheses if (1) you are on the research team and want to support the claim? (2) you are on an opposing team and want to reject the claim? 1) Because you want to support this claim, make the claim the alternate hypothesis.

0 : 96 (Claim) 2) Because you want to reject this claim, make the claim the null hypothesis. : >96 (Claim) Assignments: Classwork: Page 375 #1-22 All Homework: Pages 376-377 # 23-49 Odds

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