A college professor teaching statistics conducts a study of 1/ randomly selected students, comparing the number of homework exercises the students completed and their scores on the final exam, claiming that the more exercises a student completes, the higher their mark will be on the exam. The study yields a sample correlation coefficient of r = 0.607. Test the professor's claim at a 1% significance level.

Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of a = 0.05 Question: Determine the null and alternative hypotheses

Does more education lower a person’s level of prejudice? The number of years of education and the score on a prejudice test for ten people is given in the following table. Higher scores on the test indicate more prejudice. Years of Education 12 15 14 13 18 10 16 12 10 4 Score on Prejudice Test 1 6 2 3 2 4 1 5 5 10   Conduct a hypothesis test to determine if there is a significant linear correlation between the two variables. What is the decision for this hypothesis test?  Reject the null because the absolute value of the test statistic is greater than the critical value and the p-value is less than alpha.  Fail to reject the null because the absolute value of the test statistic is less than the critical value and the p-value is greater than alpha.  Reject the null because the absolute value of the test statistic is less than the critical value and the p-value is less than alpha.  Fail to reject the null because the absolute value of the test statistic is greater than the…

. Dr. Hafen is doing research on the effects of study time (how many minutes students study) on test performance (their score on an exam).  He hypothesizes that the amount of study time will impact an individual’s performance on the exam.  Then Dr. Hafen collects data on 100 students.  He collects data on their ‘study time’ and their ‘exam performance’, then runs a Pearson correlation.  In your own words, please describe what Dr. Hafen’s null hypothesis would be and what Dr. Hafen’s alternative hypothesis would be.  If Dr. Hafen makes a Type I error, what would that mean in the context of this study?  If he makes a Type II error, what would that mean in the context of this study?