chapter10 - Chapter 10 Testing Claims Regarding a Parameter...

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493 Chapter 10 Testing Claims Regarding a Parameter 10.1 The Language of Hypothesis Testing 1. A Type I error is the error of rejecting 0 H when in fact 0 H is true. A Type II error is the error of not rejecting 0 H when in fact 1 H is true. 2. The probability of making a Type I error is α so we should choose 01 . 0 = to minimize the chance that we make a Type I error. 3. As we decrease (the probability of rejecting a true 0 H ), we are effectively making it less likely that we will reject 0 H since we require stronger evidence against 0 H as decreases. This means that it is also more likely that we will fail to reject 0 H when 1 H is really true, so β increases. Thus, increases as decreases. 4. Probability of Type I error 0.05 = = . 5. In a hypothesis test we make a judgement about the validity of a hypothesis based on the available data. If the data contradicts 0 H then we reject 0 H . However, if the available data do not contradict 0 H , this does not guarantee that 0 H is true. Consider the court system in the U.S., where suspects are assumed to be innocent until proven guilty. An acquittal does not mean the suspect is innocent, merely that there was not enough evidence to reject the assumption of innocence. 6. Reasonable doubt is based on logic and reasoning. The phrase “beyond all reasonable doubt” means that there is sufficient and convincing evidence that a reasonable person would not hesitate to act upon it. It is not based on circumstantial evidence or unsubstantiated accusations. The primary difference is that “beyond all doubt” expects every possibility to be considered while “beyond all reasonable doubt” expects that all reasonably likely possibilities have been taken into account. 7. False; sample evidence will never prove a null hypothesis is true. We assume the null is true and try to gather enough evidence to say that the null is not true. Failing to reject a null hypothesis does not imply that the hypothesis is actually true, just that there was not enough evidence to reject the assumption that it is true. 8. False; decreasing the probability of making one type of error will increase the probability of making the other type (see #3 above). 9. Parameter μ = . Right-tailed since 1 :5 H > 10. Parameter p = . Left-tailed since 1 :0 . 2 Hp < 11. Parameter σ = . Two-tailed since 1 :4 . 2 H
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Chapter 10 Testing Claims Regarding a Parameter 494 12. Parameter p = . Right-tailed since 1 :0 . 7 6 Hp > 13. Parameter μ = . Left-tailed since 1 : 120 H < 14. Parameter σ = . Two-tailed since 1 :7 . 8 H 15. (a) 0 : 0.118 = , 1 : 0.118 < The alternative hypothesis is < because the sociologist believes the percent has decreased. (b) We make a Type I error if the sample evidence leads us to reject 0 H and believe that the percentage of registered births to teenage mothers is less than 11.8% when, in fact, it is not less than 11.8%.
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chapter10 - Chapter 10 Testing Claims Regarding a Parameter...

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