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Warm UP

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Warm UP

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  1. FIRST Open the yellow books to page 4801. What is a type I error?2. What is a type II error?3. If you are diagnosed with Cancer when in fact you don’t have it, what type of error occurred?4. If you were in court for robbery and the jury said you were not guilty but in fact you did rob the bank, what type of error occurred? Warm UP

  2. review

  3. p and : • problems about proportions and percents • Sample size: np>10 & n(1-p)>10 • Standard deviation : • Same hypothesis tests and confidence intervals • μ and x: • Problems about means and averages • Sample size: as large as possible. • Standard deviation: • Same hypothesis tests and confidence intervals P or μ

  4. standard deviation: When testing a hypothesis σ standard error: when finding confidence interval or margin of error CI margin of error = σ : standard deviation or s : standard error OR

  5. Writing your conclusion p-value level of significance Enough support or not enough supportreject or fail to reject REJECT HO: With a P-value of 0.02 there is sufficient evidence at the 0.05 level of significance to support claim that the average high school student sends more than 10 texts a day. We reject the null hypothesis FAIL TO REJECT HO: With a p-value of 0.47 there is notsufficient evidence to support the claim that students send more than 10 texts a day. We fail to reject the null hypothesis

  6. One sidedor two sided test?

  7. One sided test

  8. two sided test Accept H0 Reject H0 0.025 Reject H0 0.025 0.95 Z

  9. Rejection Region for different HA a Level of significance = a a /2 /2 HA: μ≠ Rejection region is shaded Two-tail test 0 a HA: μ > 0 Upper-tail test a HA: μ < Lower-tail test 0

  10. Type I & Type II Errors

  11. Type I Error • The mistake of rejecting the null hypothesis when it is true. • The probability of doing this is called the significance level, denoted by a (alpha). • Common choices for a: 0.05 and 0.01 • Example: sending someone to jail who is not guilty Rubin Carter was a famous boxer that was arrested for the murder of several men Convicted in 1966. Case dismissed 1988

  12. Type II Error • the mistake of failing to reject the null hypothesis when it is false. • denoted by ß (beta) • Example: setting someone free who in fact committed the crime.

  13. clicker problems Which of these is a correct alternative hypothesis for a two‐tailed test? a) H a: μ ≠ 7 b) H a: μ < 7 c) H a: μ > 7

  14. The proportion of defective items is not allowed to be over 15%. A buyer wants to test whether the proportion of defectives exceeds the allowable limit. The buyer takes a random sample of 100 items and finds that 19 are defective. State the null and alternative hypotheses for this test. a) H0: p ≤ .15, H1: p > .15 b) H0: p < .15, H1: p > .15 c) H0: p = .15, H1: p * .15 d) H0: p < .15, H1: p > .15 e) none of the above

  15. How will the area of the rejection region for a two‐tailed test compare to area of the rejection of the corresponding one‐tailed test with the same significance level? a) the area will be smaller b) the area will be the same c) the area will be larger

  16. Example: 25 people treated with a statin, a cholesteral lowering medicaiton, and 25 with a placebo. Average cholesterol after treatment is 180 with statins and 200 with placebo. The standard deviation is 8. Do we have sufficient evidence to suggest that statins lower cholesterol at the 0.05 significance level? On your white boards write down the Ho and HA. Is the test one sided or two sided (click in 1 or 2)? What is the p-value? Do you reject Ho? (1 yes 2 no)

  17. Partner Quiz Time

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