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Statistics Worksheet #2 P-VALUES Name ______________________________ 1. A significance test looks for evidence against the ……………… hypothesis and in favor of the ……………… hypothesis. 2. The P-value is the probability that we would see a sample outcome as extreme or more extreme than the actually observed outcome if the ………………… hypothesis really were true. 3. The smaller the P-value is, the ………………… is the evidence against H 0 that is provided by the data. (stronger/weaker) 4. For each of the following situations, determine if we will reject or fail to reject H0. HYPOTHESES SIGNIFICANCE LEVEL P-VALUE a. H0: p = 0.5 Ha: p > 0.5 α = 0.05 P-value = 0.0325 b. H0: p = 0.5 Ha: p > 0.5 α = 0.01 P-value = 0.0325 DECISION For #5-9: If a die is fair, then the number 5 should occur 1/6 of the time. You have a die that you suspect is loaded so that the number 5 lands face up more often then expected. You roll the die 200 times and get 45 5's. Do we have evidence that the die is unfair (i.e. loaded)? 5. H0: ……………, Ha: ……………… 6. mean = …………, standard deviation = ………… observation = p̂ = ………… 7. Then standardized z- score = ……….. The P-value is …………… 8. Therefore, at α = 0.05 significance level, we would conclude which of the following: a. There is strong evidence that the die is unfair. b. There is insufficient evidence to determine whether the die is fair or unfair. 9. If we used α = 0.01 significance level, would the same choice be correct? ……… For #10-14: The White House press secretary comments that the president currently has a 72% favorable job approval rating. A pollster challenges this claim as being too high. His polling service has just conducted a random survey of 1000 people (calling both landline and cell phone numbers) and 680 people gave the president a favorable job approval rating. Do we have reason to doubt the press secretary? 10. H0: ……………, Ha: ……………… 11. mean = …………, standard deviation = ………… observation = p̂ = ………… 12. Then standardized z- score = ……….. The P-value is …………… 13. Therefore, at α = 0.05 significance level, we would conclude which of the following: a. There is strong evidence that the true favorable job approval rating is less than 72%. b. There is insufficient evidence to determine whether the true favorable job approval rating is less than 72%.. 14. If we used α = 0.01 significance level, would the same choice be correct? ……… 15. According to Sallie Mae, seventy-six percent of undergraduates had at least one credit card in 2004. In 2008, Sallie Mae took a survey of 280 undergraduates and found that 235 of these students had at least one credit card. Is there evidence that the proportion of all undergraduates with at least one credit card has increased in the four-year period? a. p̂ ……………… b. H0: ……………… c. Ha: ……………… Describe the sampling distribution: …………………………………………………………… ………………………………………………………………………………………………………………………… d. standardized score = P-value = ………… e. Conclusion: ………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………