Homework: MAT 200 Week 6 Question 20, 6.2.32-T HW Score: 76.28%, 22.88 of Homework (Graded 30 points Part 1 of 3 Assignment) Points: 0 of 1 Save The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean. 100,308 81,361 78,388 67.459 51,703 67,476 94,308 65,812 - 79,720 73,835 44,430 86,188 61,180 58,065 54,555 78,863 47,341 98,386 81.115 93,213 63,329 75,096 50,753 60,639 92,045 83,834 79.669 64,359 74,328 56,897 47.048 88.888 75.685 62, 158 82,721 (a) Find the sample mean x= (Type an integer or decimal rounded to two decimal places as neededHomework: MAT 200 Week 6 HW Score: 76.28%, 22.88 of = Homework (Graded Question 25, 6.3.17-T 30 points Assignment) Part 1 of 3 Points: 0 of 1 Save A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 2% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed (b) Find the minimum sample size needed, using a prior study that found that 32% of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? n = | |(Round up to the nearest whole number as needed.)