1. Let's assume that the hair color factor for the class was collected from one-hundred ra Statistics from ASUeven though we know the data was not truly randomly collected this semester's classes. a. First, determine from this sample data the proportion (percentage) of stud b. Explain why it would be wrong to use the proportion calculated above (e the proportion value for ALLASU Element of Statistics students who ha c. Next, based upon a 95% level of confidence, determine the margin of err ASU Element of Statistics students with brown hair from this sample dat d. Next use your margin of error value to produce the 95% confidence inter from the sample results. State this interval below within an interpretive s 2. Clearly explain the intent/meaning of the \"95%\" number in the confidence interval pro 3. As above, let's assume that the sample data for the height variable was collected from Statistics from ASU. a. Determine the mean, median, midrange, standard deviation, and variance b. Determine the margin of error in estimating the population mean height f of confidence. (You may assume that previous research has demonstrated measures of similar groups of people is 10.2 cm and that the distribution distribution). c. Using your margin of error value from (3b), give the 90% confidence int predicted from this sample's results. State this interval below within an in d. Although similar, what makes this situation in problem #3 (and hence som different from the situation in problem #1 above? 4. Notice (from the margin of error measurment determined in 3b) that we have used a s sufficiently confident that the sample mean would estimate the population mean heigh cm was much smaller than 4 cm. Therefore, determine the smaller sample size req students based upon a needed 90% confidence level with an error of no more than 4 c Does it seem reasonable that collecting a random sample of the size you determ there any issues with going to such a small sample size? Explain your position. s collected from one-hundred randomly selected people taking Elements of was not truly randomly collected but instead comes from a convenience sample of e proportion (percentage) of students which have brown hair. e proportion calculated above (even if the data came from a random sample) as ent of Statistics students who have brown hair color. nce, determine the margin of error in estimating the true population proportion of brown hair from this sample data. Give this margin of error value below. oduce the 95% confidence interval for the population proportion as predicted l below within an interpretive sentence tied to the given context. er in the confidence interval problem above. ght variable was collected from randomly selected students taking Elements of standard deviation, and variance of the "height" data. ng the population mean height from this sample's mean based upon a 90% level vious research has demonstrated the population standard deviation on height 0.2 cm and that the distribution of height measures is roughly a normal b), give the 90% confidence interval for the population mean height measure as e this interval below within an interpretive sentence. on in problem #3 (and hence some of the resulting statistical formulas used) 1 above? ed in 3b) that we have used a sample size larger than needed in order to be mate the population mean height within 4 cm; that is our margin of error at 1.678 ne the smaller sample size required to predict the mean height of all ASU stats with an error of no more than 4 cm. (Again assume = 10.2 cm.) m sample of the size you determined can produce the desire accuracy? Are ple size? Explain your position. Elements of Statistics Class Data, ---CLEANED Data Individual ID# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Gender Female Male Female Male Female Female Male Female Female Female Female Male Male Female Male Female Male Male Male Female Male Male Male Male Male Female Female Female Female Female Male Female Female Male Female Male Female Female Female Male Male Foot Length Height 24.5 25.5 23 25.5 24 25 31 24.5 21 23 25.5 27 27 22.5 27 24.5 31 26 29 24 28 26 26.5 24 27 25.5 24 24 25 24.5 27.5 20 20.5 24 21.5 32 25 25 23.5 27.5 27.5 162.5 175.5 160 175 158 163 186 165 155 165 172 168 175.5 158 188.5 162.5 183 162.5 180.5 171 180.5 180.5 176 175 173 165.5 160 161.5 174 165 178 164 153 183 162.5 178 178 168.5 162.5 185.5 176.5 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 Male Female Female Female Male Female Male Male Female Female Female Female Female Female Female Female Female Female Male Male Female Female Male Female Female Female Female Female Female Female Female Female Female Female 27 23 23 22.5 27 28 28 26.5 25 24 23 25 23 22 23.5 21 24 23.5 28 25 24 24 28 24 25 24 25.5 25.5 25 26 25 26 26 24 188 167 155 160.5 173 177.5 180 178 171.5 168 164.5 170.5 168 160.5 165 157 161.5 157.5 173 172.5 171 162.5 183.5 173.5 170 175.5 170 175 165 173 170.5 176 176.5 170 77 78 79 80 81 82 83 84 85 86 87 88 Male Male Male Male Male Female Male Male Female Female Female Female 25.5 29 27.9 29.5 29.5 25 25 25 24 24 24 25 181 177 185.5 198.5 183 172.5 180 172 160 165 160 157.5 89 90 91 92 93 94 95 96 97 98 99 100 101 Female Male Female Female Female Female Male Male Male Female Female Female Female 24.5 28 25 23 23.5 25 19 30.5 26.5 24 24.5 23.5 25.5 161 185.5 162 165 162 167.5 190.5 188 175.5 167.5 170 160 173.5 Data Age Armspan 27 31 30 29 25 22 30 18 27 24 37 28 26 32 22 46 26 47 50 27 36 36 21 28 31 20 47 24 22 29 48 43 9 22 31 37 34 23 35 31 29 156.5 187 162 175 157 163 190 166 150.5 150 172 169 184.5 162.5 187 165 188 163 182 164 183 183 176.5 172.5 175 173.5 182.5 160 169 167.5 178 161.5 151.5 188 158 165 173.5 168 161.5 181 170.5 Number in Family Hair Color 3 4 5 3 7 3 3 9 4 3 2 4 5 4 4 6 4 3 4 4 3 3 9 4 3 3 2 7 3 5 4 4 5 1 3 3 4 4 5 4 4 Blonde Black Brown Brown Brown Black Brown Brown Brown Black Black Black Brown Black Brown Brown Brown Brown Brown Blonde Black Brown Brown Blonde Black Blonde Black Blonde Brown Brown Brown Blonde Brown Brown Blonde Brown Brown Brown Red Brown Brown Black Red Brown Blonde Bald 12 6 58 23 1 100 37 20 28 27 34 41 33 32 21 14 23 25 22 32 30 21 24 22 39 20 26 21 23 27 25 30 33 37 36 18 25 26 41 20 188 154 157.5 163 173 175 189 172.5 168.5 168 166 174 160 162.5 157 158 160 160 160 161 162 158.5 183 167.5 190 170 170 170 172.5 173 174 177 178 178 3 4 4 5 3 3 3 2 3 4 4 2 4 6 5 3 7 2 6 4 5 4 5 5 5 3 4 5 4 4 2 6 9 5 Black Red Brown Brown Brown Brown Blonde Red Blonde Blonde Brown Blonde Brown Brown Brown Brown Blonde Brown Brown Black Brown Brown Brown Blonde Brown Blonde Brown Blonde Blonde Brown Blonde Brown Blonde Red 29 25 21 25 38 27 33 33 20 21 24 37 179.5 187 190.5 190.5 187.5 172.5 183 182 158 164 155 152.5 9 3 3 7 4 3 1 6 4 4 4 3 Brown Brown Brown Brown Bald Red Brown Blonde Brown Blonde Blonde Blonde 22 28 44 20 27 33 28 22 28 29 35 21 33 154 188.5 166 141 164 160 191 190.5 174 170.5 170 157.5 174.5 5 4 4 6 4 5 5 3 9 2 8 4 3 Brown Brown Brown Brown Brown Brown Black Brown Brown Red Brown Brown Blonde