Question 2 At a stop sign, some drivers come to a full stop, some come to a rolling stop' (not a full stop, but slow down), and some do not stop at all. We would like to test if there is an association between gender and type of stop (full, rolling, or no stop). We collect data by standing a few feet from a stop sign and taking note of type of stop and the gender of the driver. What are the hypotheses for testing for an association between gender and type of stop? O Ho: Males and females are equally likely to come to a full stop. H, : Males and females are not equally likely to come to a full stop. O Ho: Gender and type of stop are associated. H1: Gender and type of stop are independent. Ho: Gender and type of stop are independent. H1 : Gender and type of stop are associated. O Ho: Males and females are equally likely to come to a rolling stop. Hi: Males are more likely than females to come to a rolling stop. Submit QuestionYou are conducting a test of independence for the claim that there is an association between the row variable and the column variable. X Y Z A 35 48 B 19 52 51 The expected observations for this table would be X Z What is the chi-square test-statistic for this data? Report all answers accurate to 3 decimal places. Submit QuestionMigraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 164 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 65 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 99 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use o = Pain Free: Yes | Pain Free: No Total Treatment 15 50 65 Control 6 93 99 Total 21 143 164 a) What is the correct null hypothesis? O Ho: P1 / P2 7 P3 7 O Ho: Migraine pain relief is dependent on receiving acupuncture O Ho: Migraine pain relief is independent on receiving acupuncture. O Ho: P1 - P2 - P3 = P4 b) Fill in the expected values, round answers to at least 4 decimal places. Expected Values Pain Free: Yes Pain Free: No Treatment Control c) Find the test statistic, rounding your answer to 3 decimal places. d) Find the p-value, rounding your answer to 4 decimal places. e) What is the correct conclusion? There is statistical evidence that migraine pain relief is dependent on receiving acupuncture. There is not statistical evidence that migraine pain relief is independent of receiving acupuncture. There is not statistical evidence that migraine pain relief is dependent on receiving acupuncture. There is statistical evidence that migraine pain relief is independent of receiving acupuncture. Submit Question O Search