Inference on Two Samples and Inference on the Least Squares Regression Line

1. Determine if the following sampling is dependent or independent and whether the response variable is qualitative or quantitative. A researcher wishes to compare personality types of brothers and sisters. She obtains a random sample of 583 pairs of siblings who take a personality inventory and determines each sibling's personality type. 2. To test the belief that sons are taller than their fathers, a student randomly selects 5 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the a = 0.025 level of signicance. Assume the differences are normally distributed. Height of Height of Father. Xi Son, Y; 67.1 72.0 71.9 75.4 70.1 72.6 73.3 75.1 73.3 74.4 a. Is this a dependent or independent sample? What conditions must be met to perform this test? b. Let d: = X: Yi. Write the null and altemative hypotheses for this test. c. Calculate the test statistic using the fact that d = 2.76 and sd = 1.489 and nd the P-value range. d. Should the null hypotheses be rejected at the a = 0.025 level of significance? e. Construct a 95 % confidence interval with this data. 3. A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain year, monitoring the progress the students made toward completing a bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a bachelor's degree than those who immediately attended and remained at a 4-year institution. The data in the table below summarize the results of his study. Does the evidence suggest that community college transfer students take longer to attain a bachelor's degree? Community No Transfer College Transfer n 258 1148 Sample mean time to 5.37 4.29 graduate, in years Sample standard 1.146 1.013 deviation time to graduate, in years a. What is the response variable and what is the explanatory variable? b. Determine what qualifications are met to perform the hypothesis test about the difference between two means. 2c. Determine the null and alternative hypotheses. d. Determine the test statistic. e. Suppose the p-value of this test is equal to 000, state the conclusion at an a = 0.10 level of signicance. f. Construct a 95 % condence interval for \"community college ,um, transfer to approximate the mean additional time it takes to complete a bachelor's degree if you begin in community college. (Using d f = 352) 4. Suppose a lest-squares regression line is given by j} = 4.302): 3293. What is the mean value of the repose variable if x = 20