Measuring Evidence with p-values Section 4.2 Measuring Evidence with p-values

Green Tea and Prostate Cancer A study was conducted on 60 men with PIN lesions, some of which turn into prostate cancer Half of these men were randomized to take 600 mg of green tea extract daily, while the other half were given a placebo pill The study was double-blind, neither the participants nor the doctors knew who was actually receiving green tea After one year, only 1 person taking green tea had gotten cancer, while 9 taking the placebo had gotten cancer

Green Tea and Prostate Cancer The explanatory variable is green tea extract of placebo, the response variable is whether or not the person developed prostate cancer. What statistic and parameter is most relevant? Mean Proportion Difference in means Difference in proportions Correlation Two categorical variables

Review State the null hypotheses. H0: p1 = p2 H0: p1 < p2 p1 = proportion of green tea consumers to get prostate cancer p2 = proportion of placebo consumers to get prostate cancer State the null hypotheses. H0: p1 = p2 H0: p1 < p2 H0: p1 > p2 H0: p1 ≠ p2 The null hypothesis always includes an equals sign.

Review State the alternative hypotheses. Ha: p1 = p2 Ha: p1 < p2 p1 = proportion of green tea consumers to get prostate cancer p2 = proportion of placebo consumers to get prostate cancer State the alternative hypotheses. Ha: p1 = p2 Ha: p1 < p2 Ha: p1 > p2 Ha: p1 ≠ p2 The alternative hypothesis is what the researchers are aiming to prove.

Randomization Distribution Based on the randomization distribution, would the observed statistic of -0.267 be extreme if the null hypothesis were true? Yes No

Randomization Distribution Do you think the null hypothesis is a plausible explanation for these results? Yes No

Randomization Distribution In a hypothesis test for H0:  = 12 vs Ha:  < 12, we have a sample with n = 45 and 𝑥 =10.2 . What do we require about the method to produce randomization samples? We need to generate randomization samples assuming the null hypothesis is true.  = 12  < 12 𝑥 =10.2

Randomization Distribution In a hypothesis test for H0:  = 12 vs Ha:  < 12, we have a sample with n = 45 and 𝑥 =10.2. Where will the randomization distribution be centered? Randomization distributions are always centered around the null hypothesized value. 10.2 12 45 1.8

Randomization Distribution In a hypothesis test for H0:  = 12 vs Ha:  < 12, we have a sample with n = 45 and 𝑥 =10.2. What will we look for on the randomization distribution? We want to see how extreme the observed statistic is. How extreme 10.2 is How extreme 12 is How extreme 45 is What the standard error is How many randomization samples we collected

Randomization Distribution In a hypothesis test for H0: 1 = 2 vs Ha: 1 > 2 , we have a sample with 𝑥 1 =26, 𝑥 2 =21. What do we require about the method to produce randomization samples? We need to generate randomization samples assuming the null hypothesis is true. 1 = 2 1 > 2 𝑥 1 =26, 𝑥 2 =21 𝑥 1 − 𝑥 2 =5

Randomization Distribution In a hypothesis test for H0: 1 = 2 vs Ha: 1 > 2 , we have a sample with 𝑥 1 =26, 𝑥 2 =21. Where will the randomization distribution be centered? The randomization distribution is centered around the null hypothesized value, 1 - 2 = 0 1 21 26 5

Randomization Distribution In a hypothesis test for H0: 1 = 2 vs Ha: 1 > 2 , we have a sample with 𝑥 1 =26, 𝑥 2 =21. What do we look for on the randomization distribution? We want to see how extreme the observed difference in means is. The standard error The center point How extreme 26 is How extreme 21 is How extreme 5 is

A randomization distribution is shown to test H0 :  = 0 vs Ha :  > 0 If r = 0.1, the p-value is closest to A. 0.005 B. 0.01 C. 0.1 D. 0.2 E. 0.4

A randomization distribution is shown to test H0 :  = 0 vs Ha :  > 0 If r = 0.5, the p-value is closest to A. 0.005 B. 0.1 C. 0.25 D. 0.4 E. 0.7

A randomization distribution is shown to test H0 :  = 0 vs Ha :  > 0 If r = 0.25, the p-value is closest to A. 0.005 B. 0.1 C. 0.25 D. 0.4 E. 0.7

A randomization distribution is shown to test H0 :  = 0 vs Ha :  > 0 If r = – 0.2, the p-value is closest to A. 0.005 B. 0.1 C. 0.25 D. 0.4 E. 0.7