Does ones regional location have an affect on their Political affiliation? To begin to investigate this situation data from 177 random voters was analyzed. Political Affiliation Democrat Republican West 39 27 Northeast 35 15 Southeast 17 44 a.) Find the Proportion of Democrats among each regional location. b.) Make a Bar Chart for these Prop. c.) Find the Expected Values for each cell. d.) Find evidence of an affect. 33.93 0.591 32.07 Location 25.71 0.700 24.29 31.36 0.279 29.64 0 50 100 % of Dem. W NE SE Regional Location

Does ones regional location have an affect on their Political affiliation? To begin to investigate this situation data from 177 random voters was analyzed. Political Affiliation Democrat Republican West 39 27 Northeast 35 15 Southeast 17 44 d.) Find evidence of an affect. 33.93 32.07 Location 25.71 24.29 31.36 29.64 X2 Test of Independence H0: Political Affiliation is INDEPENDENT of Location Ha: Political Affiliation is NOT INDEPENDENT of Location P-Value = X2cdf (22.01, E99, 2) = 0 X2 = 22.01 Since the P-Value is less than α = 0.05 we will REJECT H0 . There is evidence that Political Affiliation is NOT INDEPENDENT of Location. SRS – stated All Expected Counts are 5 or greater.

d.) How does the X2 in (c) relate to the z in (b)? What is the relationship between a 2-Proportion Z-Test and a X2-Test? To investigate, answer the following about the Titanic: Female Male Alive 343 367 Dead 127 1364 TOTAL 470 1731 0.730 0.212 a.) Find the Proportion of Females and Males that Survived the Titanic. b.) Determine whether or not there was a significant difference between the survival of a Female and a Male by conducting a 2-Prop Z-Test. c.) Determine whether or not gender is independent of survival by conducting a X2-Test. d.) How does the X2 in (c) relate to the z in (b)?

z = 21.295 X2 = 453.476 H0: pm = pw Ha: pm ≠ pw P-Value = 0 b.) pi = The true proportion of each gender that survived the titanic. pm = Men and pw = Women z = 21.295 H0: pm = pw Ha: pm ≠ pw TWO Proportion z – Test P-Value = 0 Since the P-Value is less than α = 0.05 the data IS significant . There is STRONG evidence to REJECT H0 . The proportion of men who survived does differs from that of women. c.) H0: Gender is independent to survival. Ha: There is an association between gender and survival. X2 = 453.476 P-Value = 0 Since the P-Value is less than α = 0.05 the data IS significant . There is strong evidence to REJECT H0 . There is strong evidence that suggests that gender is associated to survival. d.) (z = 21.295)2 = (X2 = 453.476)

#18 Medical researchers followed an SRS of 6272 Swedish men for 30 years to see if there was an association between the amount of fish in their diet and Prostate Cancer. Is there any evidence of such an association? Fish Consumption Total Subjects Prostate Cancer Never 124 14 Small part of diet 2621 201 Moderate part 2978 209 Large part 549 42 9.21 114.79 194.74 2426.26 221.26 2756.74 40.79 508.21 NO Prostate Cancer 14 110 201 2420 209 2769 42 507 H0: There is NO relationship between fish consumption and the development of Prostate Cancer. Ha: There is relationship between fish consumption and the development of Prostate Cancer. X2 Test of Independence P-Value = X2cdf (3.677, E99, 3) = 0.2985 X2 = 3.677

WARM – UP Medical researchers followed 6272 Swedish men for 30 years to see if there was an association between the amount of fish in their diet and Prostate Cancer. Is there any evidence of such an association? Fish Consumption Total Subjects Prostate Cancer Never 124 14 Small part of diet 2621 201 Moderate part 2978 209 Large part 549 42 9.21 114.79 194.74 2426.26 221.26 2756.74 40.79 508.21 NO Prostate Cancer 14 110 201 2420 209 2769 42 507 H0: There is NO relationship between fish consumption and the development of Prostate Cancer. Ha: There is relationship between fish consumption and the development of Prostate Cancer. X2 Test of Independence P-Value = X2cdf (3.677, E99, 3) = 0.2985 X2 = 3.677 CONDITIONS SRS - Stated √ All Expected Counts are 1 or greater. √ No more than 20% of the Expected Counts are less than 5. √ Since the P-Value is NOT less than α = 0.05 there is NO evidence to reject H0. There is NO evidence of a relationship between fish consumption and Prostate Cancer.

Warm-Up: The maker of Trick Dice sells you a weighted die in which “5” is supposed to show up 35% of the time with the other outcomes equally divided among the rest of the time. You roll the die 200 times. Based on the following results, is the die in question really a weighted die favoring ‘5’? 1 2 3 4 5 6 OBS. DATA 26 35 20 55 29 X2 Goodness of Fit Test EXP. DATA 26 70 H0: The die is weighted so that ‘5’ appears 35% of the time! Ha: The die is NOT weighted so that ‘5’ appears 35% of the time! X2 = 11.176 P-Value = 0.0480

All Expected Counts are 1 or greater. Since the P-Value is less than α = 0.05 there is evidence to REJECT H0 . There is evidence that the die is NOT weighted as indicated by the Trick Dice maker. CONDITIONS SRS – randomly tossed All Expected Counts are 1 or greater. No more than 20% of the Expected Counts are less than 5. EXP. DATA 26 70