Ii i tossing a fair coin 100 times and getting between

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Unformatted text preview: 2 3 4 6 The SD of the box is 2. € a) The Expected Value for the average of the 100 draws is _____3________. Average of box = 3 so EVave of the draws = 3 b) The Standard Error of the average of the 100 draws is ___0.2__________. SEave = SD 2 = = 0.2 n 100 c) The Expected value for the percent of 6 ’s in 100 draws is _____20%________. € € 20% of the box is 6 ’s so EV% = 20% d) The Standard Error for the percent of 6 ’s in 100 draws is _____4%________. (HINT: Change to 0 ­1 box) Change the box to 4 0 ’s and 1 1 SD = € 0.4 41 x 100% = 4% × = 0.4 so SD% = 55 100 € Page 5 Study Guide KEY for Exam 3 2) A fair coin is tossed n times. a)What is the box model? Box has 1 ticket marked “0” and 1 ticket marked “1”. b)What is the average and the SD of the box? Ave of box = 0.5 and the SD of box = 11 × = .5 22 c) Fill in the following chart for the EV and SE of the number (sum) and the percent of heads in n tosses, the first 2 rows are done for you : € n = # of tosses EVsum SEsum EV% SE% 100 50 5 50% 5% 100 x 4 = 400 200 5 x 4 = 10 50% 5% ÷ 4 =2.5% 100 x 16= 1600 800 5 x 16 = 20 50% 5% ÷ 16 = 1.25 % 100 x 25=2500 1250 € 5 x 25 = 25 50% € 5% ÷ 25 = 1 % 100 x 100 = 10,000 5,000 € 5 x 100 = 50 50% € 5% ÷ 100 = 0.5 % € € d) For the following questions circle the more likely possibility. If they’re equally likely circle both: € € i) (i) Tossing a fair coin 100 times and getting 50+/ ­ 5 heads (between 45 ­55 heads) (ii) Tossing a fair coin 10,000 times and getting 5000 +/ ­ 5 heads (between 4995 and 5005 heads) More draws means more error as a number (SEsum) so you’d expect to have more than +/ 5 error with 10,000 draws. ii) (i) Tossing a fair coin 100 times and getting between 50% +/ ­ 5% heads (between 45% ­55% heads.) (ii) Tossing a fair coin 10,000 times and getting 50% +/ ­ 5% heads (between 45% ­55% heads.) More draws means less error as a % (SE%) so you’d expect to get closer to 50% heads with more draws. iii) (i) Tossing a fair coin 100 times and getting 50+/ ­ 5 heads (between 45 ­55 heads) (ii) Tossing a fair coin 10,000 times and getting 5000 +/ ­ 50 heads (between 4950 and 5050 heads) Equally likely, both have the same SEsum (See table ab...
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