Activity 1 - Simple Random and Stratified Random Samples SP 14(4)(1) E

Activity 1 - Simple Random and Stratified Random Samples SP 14(4)(1) E STAT 1350: Elementary Statistics Collaborative Activity 1 Simple Random and Stratified Random Sampling Sampling Frame The sampling frame provided with this Collaborative Activity represents the student body as of the first day of autumn semester at a small liberal arts school in central Ohio. A Simple Random Sample The college believes that 75% of the student body resides on campus. Use the random number table (attached) to randomly select 10 students. Label the sampling frame using two digit numbers. STEP 1: Label the Sampling Frame STEP 2: Generate Random Numbers starting at row 145 of Table A a. List the 10 students. Indicate whether the student resides on campus or commutes to campus. |Label Number |Dorm or Off Campus|Label Number |Dorm or Off Campus| | | | | | | | | | | | | | | | | | | | | | | | | | b. What percentage of your SRS live in a dorm? ________________________ c. I selected 5 other SRS of size 10 and recorded the percentage of each sample who lives in a dorm. Compare your percentage from part (b) to the percentages given below. Explain why the percentages are not all the same. 30%; 20%; 30%; 40%; 40%; d. Does your data support the college's belief? Explain why or why not. Stratified Simple Random Sample - a variation of the SRS. To take a Stratified Simple Random Sample, divide the population into 2 or more strata (naturally occurring subgroups). Take a SRS from the first strata then take a SRS from the second strata and so on until you have a SRS from each of the strata. Combine the SRS selected from each strata to make your stratified simple random sample. Pick a stratified sample, by gender of 20 students. Select 10 students from each stratum and record the class rank of each student. First select a SRS of 10 females. Then, continuing on the random number table where you left off, select a SRS of 10 males. Use the labels as you assigned them for the first SRS. STEP 1: Female labels: ____________________ Male: _______________________ STEP 2: Start at row 137 of Table A. a. List the 20 students |Label Number|Gender |Class Rank |Label Number|Gender |Class Rank | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | | |Female | | |Male | | What does your sample reveal about class rank and gender? Answer in complete sentence(s). TABLE A Random digits Line 101 19223 95034 05756 28713 96409 12531 42544 82853 102 73676 47150 99400 01927 27754 42648 82425 36290 103 45467 71709 77558 00095 32863 29485 82226 90056 104 52711 38889 93074 60227 40011 85848 48767 52573 105 95592 94007 69971 91481 60779 53791 17297 59335 106 68417 35013 15529 72765 85089 57067 50211 47487 107 82739 57890 20807 47511 81676 55300 94383 14893 108 60940 72024 17868 24943 61790 90656 87964 18883 109 36009 19365 15412 39638 85453 46816 83485 41979 110 38448 48789 18338 24697 39364 42006 76688 08708 111 81486 69487 60513 09297 00412 71238 27649 39950 112 59636 88804 04634 71197 19352 73089 84898 45785 113 62568 70206 40325 03699 71080 22553 11486 11776 114 45149 32992 75730 66280 03819 56202 02938 70915 115 61041 77684 94322 24709 73698 14526 31893 32592 116 14459 26056 31424 80371 65103 62253 50490 61181 117 38167 98532 62183 70632 23417 26185 41448 75532 118 73190 32533 04470 29669 84407 90785 65956 86382 119 95857 07118 87664 92099 58806 66979 98624 84826 120 35476 55972 39421 65850 04266 35435 43742 11937 121 71487 09984 29077 14863 61683 47052 62224 51025 122 13873 81598 95052 90908 73592 75186 87136 95761 123 54580 81507 27102 56027 55892 33063 41842 81868 124 71035 09001 43367 49497 72719 96758 27611 91596 125 96746 12149 37823 71868 18442 35119 62103 39244 126 96927 19931 36089 74192 77567 88741 48409 41903 127 43909 99477 25330 64359 40085 16925 85117 36071 128 15689 14227 06565 14374 13352 49367 81982 87209 129 36759 58984 68288 22913 18638 54303 00795 08727 130 69051 64817 87174 09517 84534 06489 87201 97245 131 05007 16632 81194 14873 04197 85576 45195 96565 132 68732 55259 84292 08796 43165 93739 31685 97150 133 45740 41807 65561 33302 07051 93623 18132 09547 134 27816 78416 18329 21337 35213 37741 04312 68508 135 66925 55658 39100 78458 11206 19876 87151 31260 136 08421 44753 77377 28744 75592 08563 79140 92454 137 53645 66812 61421 47836 12609 15373 98481 14592 138 66831 68908 40772 21558 47781 33586 79177 06928 139 55588 99404 70708 41098 43563 56934 48394 51719 140 12975 13258 13048 45144