b. Use the standard deviation of the first sample and apply the formula to find the standard error (SE X ) of the sample mean with a sample size of 5, a sample size of 10 and a sample size of 20 (4 points) c. Compared the 3 different SE x in part b, what can you conclude? (1 point) 9. Compute the proportion of each group in each sample for the groups in the table. Record these in the following table (10 points) Sample # Females Males Sample # Democrats Republicans 1 1 IN IN 3 4 6 6 8 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 a. Find the population proportions (p) of Female, Male, Democrats and Republicans. (4 points) b. Find the mean of all the sample proportions of Female, Male, Democrats and Republicans. (4 points) c. Use the sample #5 of the variable female and apply the formula to find the standard error (SE p^) (2 points)d. Use Rguroo to find the probability of getting the proportion of females that is more than what you got in sample #5 by Standard Normal Distribution Approach (Answer: 5 points) AND Normal Distribution Approach (5 points) e. Use the sample #18 of the variable republicans and apply the formula to find the standard error (SE p\") (2 points) f. Use Rguroo to find the probability of getting the proportion of republican that is less than what you got in sample #18 by Standard Normal Distribution Approach (5 points) AND Normal Distribution Approach (5 points) 36513 36777 46132 31330 31341 77367 34130 93793 73435 37536 41359 94193 13019 07274 32443 72430 25432 96593 69226 33655 25337 63321 33914 32707 04070 60631 01674 14751 70294 35450 73903 93066 37739 56403 92320 95929 46391 60276 67090 45063 11666 99916 40910 59063 41169 37965 39116 75635 40791 64953 07015 37132 51063 29041 33112 03311 66426 24769 64290 23637 39932 52136 77107 53545 92061 34534 35165 04594 47573 05542 19423 97402 51472 93729 61345 93129 59203 96997 03342 20496 72026 26905 36930 79503 39925 33452 70699 43591 66022 29420 94576 92130 29705 33043 27569 65353 76703 33357 40336 95266 55340 47363 34343 56313 65617 11951 34332 50000 90975 07679 42113 43263 73213 51137 05257 33775 03747 90134 23701 16224 53204 51731 33973 30312 02743 13360 49336 76039 10479 43136 96334 03406 23296 73094 74971 15275 54796 19143 21564 20092 02333 75230 97661 36721 44254 70953 73339 11547 91252 71767 91657 41454 69390 30773 36114 03002 53603 94361 62532 17411 77436 31639 12615 39313 47200 79907 59613 66635 60017 09315 33250 99134 04474 71362 43527 63222 30571 64549 63335 53949 61749 47319 56123 02457 27973 35046 54936 73176 06611 67494 72335 39723 16337 53140 43931 32909 32246 53363 30110 31173 73244 54677 42927 61035 39342 66545 00985 62413 67753 34641 35243 26501 17292 01270 00606 22223 93470 99533 74162 49595 37346 56004 52799 32044 55745 90993 31753 62273 32163 31960 35652 69630 95525 90539 93339 94457 42523 17956 06206 24364 21160 50404 50663 35912 04379 41050 00202 52540 46795 39640 94930 61363 39033 62317 10333 36316 74567 92725 39520 45323 19024 54272 99797 09411 63562 47459 15156 05133 76293 45727 62154 05947 39437 23415 22752 44374 57331 13633 37334 22633 63153 77771 63431 15319 33516 73493 44659 14033 57072 00365 57476 43995 35709 33314 01934 90044 64663 40101 23352 7. Use Rguroc or Excel lo calculate the mean of age of each sample. Record these in the following table. (5 points) Sample # a. Find the population mean {p} of the age (3 points) b. Use the 20 sample means (Sample size of 5) of the age from the table to find the mean of the sample means 37.\" of age (3 points} c. Compared (p) to if .what can you conclude? (1 point} d. Use Wm find the probability of getting the sample mean of age greater than what you got from Sample #10 by Standard Normal Distribution Approach (5 points] AND Normal Distribution Approach (5 points) 8. Use amor Excel to calculate the standard deviation of age of each sample of 3 different sample sizes. sample of 5 data. sample of 10 data and sample of 20 data. Record these in the following table. Sample # Standard Deviation of age Standard Deviation of age Standard Deviation of age [Sample of 5 data] {Sample of 'ID data} {Sample of 20 data} {Answer 5 points} (Answer 3 points} {Answer 2 points} _L (:1 _L_L_L_L LNJELIJM _L_L_L_L moo-um L 20 a. Find the population standard deviation of the sample mean (5). {1 point) SAMPLING US SENATORS Consider the members of the US Senate (as of September 2015) as the population of interest. These senators are listed below in alphabetical order, along with their sex, party, state and years of service (as of September 2015) in the Senate ID# Name Sex Party State Years Age ID# Name Sex Party State Years Age Alexander TN King ME 69 Ayotte NH 45 Kirk M R IL Baldwin WI 51 Klobuchar D MN Barrasso WY 61 Lankford M 47 Bennet co 6 48 Leahy M D 40 Blumenthal CT 67 Lee M 42 Blunt MO 63 Manchin M D Booker D NI 45 Markey M Boozman 62 Mccain M Boxer D Mccaskill Brown Mcconnell M Burr Menendez M Cantwell Merkley Capito Mikulski Cardin Moran Carper Murkowski Casey M D Murphy Cassidy Murray Coats Nelson Cochran Paul Collins Perdue Coons D Peters Corker Portman Cornyn R Reed Cotton Reid Crapo Risch Cruz Roberts Daines Rounds T 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 3 Donnelly D Rubio Durbin Sanders Enzi Sasse Ernst Schatz Feinstein D Schumer Fischer R Scott Flake Sessions Franken Shaheen Gardner Shelby Gillibrand Stabenow Graham Sullivan Grassley Tester Hatch Thune Heinrich Tillis Heitkamp D Toomey 13 M 3 3 3 3 3 3 3 3 Heller Udall Hirono D Vitter Hoeven Warner Inhofe Warren Isakson M R Whitehouse Johnson M Wicker Kaine M D Wyden M 19Questions: 1 . How can we determine if the first 10 data of the age of the senators is or is not normally distributed? (Read vertically, for example, the first data is 7'3 and the second one is 45) (10 points) If 10 senate members are randomly selected from the above table, what is the probability that 2 of them are democrats? (2 points} If 10 senate members are randomly selected from the above table, what is the probability that at least 9 of them are democrats? (5 points} If 10 senate members are randomly selected from the above table, what is the probability that at most 8 of them are democrats? (3 points) The following 2- way table shows the number of the senators in terms of their gender and the parties they belong. Fill in the blanks (3 points) Democrat Re-ublican a. What is the probability that a randomly chosen senator is a republican given that he is a male. (3 points) b. What is the probability that a randomly chosen senator is a female given that she is a democrat (3 points) Use the following random number table to select 5 members of the US. senate to go to Hong Kong to investigate the 2019 Prodemocracy Movement. Start from the second row and read the random number from left to the right (horizontally) to do the simple random sampling. Write the names of the 10 selected members. Make sure you assign the number to the members of the senate vertically. (5 points)