equal. Complete parts a through e According to the Institute for College Access & Success, the average student-loan debt for the most recent class of students from Pennsylvania is $9,000 more than the average for students in California. To test this claim, the accompanying data were collected from random samples. Assume the population variances for the student-loan debt for these two states are Pennsylvania California Sample mean $29,914 $18 265 Sample size 25 25 Sample standard deviation $8, 100 $7,200 Click the icon to view the Student's t-distribution table. a. Using a = 0.05, perform a hypothesis test to investigate the claim of the Institute for College Access & Success. dentify the null and alternative hypotheses. Choose the correct answer below. O A. Ho:H1 - H2 9,000 H1:141 - H2 =9,000 1 Tall 0.200 0.100 0.050 0.025 0.010 0.005 2 Tail 0.400 0.100 0.050 0.020 0.010 Conf Lev 0.600 0.800 0.900 0.950 0.980 0.990 Calculate the test statistic, tx. 25 0.856 1.316 1.708 2.060 2.485 2.787 26 0.856 1.315 1.706 2.056 2.479 2.779 (Type an integer or decimal rounded to two decimal places as needed.) 27 0.855 1.314 1.703 2.052 2.473 2.771 28 0.855 1.313 1.701 2.048 2.467 2.763 Determine the critical value, to. 0.854 1.311 1.699 2.045 2.756 0.854 2.750 31 0.853 2.453 2.744 ta = 32 0.853 2.037 2.449 2.738 (Type an integer or decimal rounded to three decimal places as needed.) 33 0.853 1.692 2.035 2.733 0.852 2.032 2.728 Since to V tax Ho. There sufficient evidence to conclude that the average student-loan debt for a student in Pennsylvania is $9,000 more than the average for students in California. 35 0.852 2.030 2.724 0.852 2.719 b. Approximate the p-value using the table and interpret the results. 0.851 2.715 0.851 2.024 2.712 The p-value will be between and . This interval is the alpha level of 0.05. Therefore, OH 4 0.851 2.023 2.708 0 .851 2.021 2.704 (Type integers or decimals. Do not round. Use asce ding order.) 0.850 2.020 2.701 883888 0.850 2.018 2.698 c. Construct a 95% confidence interval to estimate the average difference in the student-load debt between these two states. Interpret the result. 288388 0.850 2.017 2.695 0.850 2.692 We are 95% confident that the differ age student debt is between ]and ]. The fact that this interval ' contain 0 provides evidence that there |a difference in the average student debt. 0.850 1.301 2.015 2.690 Type integers or decim s needed.) 0.850 1:300 0.849 1.300 d. Determine the precise p-value using Excel and interpret the results. 0.849 1.299 1.677 0.849 1.299 1.677 2.010 2.405 2.680 p-value = 1849 299 .676 2.009 2:403 2.678 (Type an integer or decimal rounded to three dec the alpha level of 0.05. Therefore, we Ho. This conclusion with the conclusion made in parts a, b, and c. This p-value is Print Done e. What assumptions need to be made in order to perform this procedure? Select all that apply. A. The samples are from the same population OB. The population means are unknown and equal. C. Both of the samples are larger than 30. Click to select your answer(s). MacBook Air DD 12 20 888 esc F1 F2 F3 F4 # 5 6 8 O @ N 3 4
