6. *Is there a relationship between the number of votes received by candidates for public office and the amount spent on their campaigns? Candidate Amount spent (000) Votes received (000) Weber $3 14 Taite $4 Spencer $2 5 Lopez $5 12 Using a 0.01 significance level, do the formal hypothesis test (using critical values). Remember to show your steps (including all relevant information) 7. *A sociologist claims that the students' college GPA's in unrelated to their families' incomes. For a random sample of 20 students the coefficient of correlation was computed as 0.40. Using the 0.01 significance level, do the formal hypothesis test. Remember to show your steps (including all relevant information) * In statistics we employ a method of "proof of contradiction." Generally, we hope to prove something is true by rejecting the claim in the null hypothesis. If the sample evidence contradicts the null hypothesis, we can reject it and "believe" the alternate hypothesis. On the other hand, if the sample information does not contradict the null hypothesis, you still have not proven that the null hypothesis is true. You merely have found that the null hypothesis cannot be rejected. * If rejecting a true null hypothesis is relatively serious, then set the significance level quite low. If accepting a false null hypothesis is relatively more serious, then pick a high level of significance.1. *Statistical question: Is the proportion of inner-city families living on a subsistence income: 20%? Two hundred families were randomly selected for the survey and 38 were found to have income at the subsistence level. Use the formal critical value method at 5% level of significance. Remember to show your steps (including all relevant information) and explicitly verify that all assumptions of the procedure are satisfied. 2. *National data reveals that the probability a youthful offender on probation will commit another crime is 80%. A special rehabilitation program was conducted for youthful offenders. A sample of 100 participants showed that 75 subsequently committed another crime. Do the hypothesis using the formal critical value method at 1% level of significance: HO: p 2 0.80 H1: p