Activity 5MATH 250 Elements of StatisticsSpring 2017 DUE DATE: 03/21/2017 General Instructions: Please place your name above, then complete the following questions. NOTE: Read to get a feel for the activity before continuing. Make sure to save this Excel file often using the filename "your complete, submit your answers to this activity by attaching your Excel file through the completion link in the U assignment description in Blackboard. Use the area to the near right in this Excel worksheet when calculating Methods/work to calculate values must be shown in the spreadsheet in order to receive full credit. Overview: As discussed in the 6th and 7th Chapter of your text, one must realize the difficulty of and issues related to parameters from sample data (e.g. determine the mean height of all FHSU students but only collect a samp covered in the 2nd half of Chapter 6), one must understand sampling distributions and the related issue of the study of such distributions (also the key to truly understanding the rest of the material in the remaining of sampling distributions, then one can predict population parameters from sample statistics and have som prediction. Do note however, we can never be 100% sure of the true population value based from a sampl confident the population value is within some interval we build around a collected sample statistic. This a you use the cleaned class data from Activity 4 to predict some population parameters and to discuss issues The cleaned data set of seventy-seven values is given to the right (recall that one individual's data was elim 1. Let's assume that the hair color factor for the class was collected from seventy-seven randomly selected st Statistics at FHSUeven though we know the data was not truly randomly collected but instead comes fro this semester's various virtual sections of the course. a. First, determine from this sample data the proportion (percentage) of students which have bl 0.1038961039 b. Explain why it would be wrong to use the proportion calculated above (even if the data came the proportion value for ALL FHSU Element of Statistics students who have black hair colo This is a small sample from one stats class and not from ALL students at FHSU, c. Next, based upon a 90% level of confidence, determine the margin of error in estimating the FHSU Element of Statistics students with black hair from this sample data. Give this margin d. Next use your margin of error value to produce the 90% confidence interval for the populatio from the sample results. State this interval below within an interpretive sentence tied to the g 2. Clearly explain the intent/meaning of the \"90%\" number in the confidence interval problem above. 3. As above, let's assume that the sample data for the foot length variable was collected from randomly selec of Statistics from FHSU. a. Determine the mean, median, midrange, standard deviation, and variance of the "foot length" b. Determine the margin of error in estimating the population mean foot length from this one sa 95% level of confidence. (You may assume that previous research has demonstrated the pop foot length measures of similar groups of people is 3.4 cm and that the distribution of foot le normal distribution). c. Using your margin of error value from (3b), give the 95% confidence interval for the popula as predicted from this sample's results. State this interval below within an interpretive senten d. Although similar, what makes this situation in problem #3 (and hence some of the resulting s different from the situation in problem #1 above? 4. Notice (from the margin of error measurment determined in 3b) that we have used a sample size larger th sufficiently confident that the sample mean would estimate the population mean foot length within 1.5 cm; was much smaller than 1.5 cm. Therefore, determine the smaller sample size required to predict the m stats students based upon a needed 95% confidence level with an error of no more than 1.5 cm. (Again a Does it seem reasonable that collecting a random sample of the size you determined can produce there any issues with going to such a small sample size? Explain your position. NAME: Jessica Bennett owing questions. NOTE: Read the entire document below ile often using the filename "yournameActivity5". Once rough the completion link in the Unit 2 Activity 5 Excel worksheet when calculating any statistics/parameters. to receive full credit. the difficulty of and issues related to predicting population HSU students but only collect a sample to do so.) To do this (as distributions and the related issue of probability as found through rest of the material in the remaining chapters.) With knowledge from sample statistics and have some indication of the strength of population value based from a sample, we can only be relatively d a collected sample statistic. This activity is designed to have ion parameters and to discuss issues regarding such predictions. all that one individual's data was eliminated in Activity 4). m seventy-seven randomly selected students taking Elements of omly collected but instead comes from a convenience sample of rcentage) of students which have black hair. 8 1038961039 culated above (even if the data came from a random sample) as s students who have black hair color. ALL students at FHSU, he margin of error in estimating the true population proportion of m this sample data. Give this margin of error value below. confidence interval for the population proportion as predicted an interpretive sentence tied to the given context. ence interval problem above. e was collected from randomly selected students taking Elements on, and variance of the "foot length" data. on mean foot length from this one sample's mean based upon a s research has demonstrated the population standard deviation on m and that the distribution of foot length measures is roughly a % confidence interval for the population mean foot length measure below within an interpretive sentence. 3 (and hence some of the resulting statistical formulas used) e have used a sample size larger than needed in order to be tion mean foot length within 1.5 cm; that is our margin of error ample size required to predict the mean foot length of all FHSU or of no more than 1.5 cm. (Again assume = 3.4 cm.) e size you determined can produce the desire accuracy? Are ain your position. MATH 250- Elements of Statistics Class Data, Spring 2017---CLEANED Student Data Individual ID# Gender Foot Length Height Age Armspan 1 2 3 4 5 6 7 8 9 10 11 12 Male Male Female Male Female Male Male Female Female Female Female Female 27 25.5 24.5 28 23.5 28.5 33 23 25 25.5 24 26 169 205.5 158.5 190.5 157.5 183 193 155 165.5 160 168 171 27 32 45 32 24 33 34 20 19 23 29 33 175 189 159 198 142 174.5 190.5 166 158.5 173 167.5 171.5 13 14 15 16 17 18 19 Male Female Male Male Female Female Female 29 21.5 28.5 27.5 24 23.5 25.5 193 165 179 183 172 165 167 46 31 39 44 33 32 34 193 171 188 186.5 173 157 150.5 21 22 23 24 25 26 27 Female Female Female Female Female Female Female 24 21 21.5 20 25 23.5 21 163 162 177.5 166 170 165 157.5 28 21 22 26 26 32 39 163 155 171.5 160 162 161 157.5 28 Female 22 156 25 155 29 30 31 32 33 34 35 36 37 38 39 40 41 Female Female Male Female Male Female Male Female Male Female Female Female Female 23 23.5 28 24 28 24 30 23 27.5 24 28 23 21.5 162.5 173 182 170 165 172 188 160 180.5 162.5 167.5 163 154 23 30 41 32 14 36 21 29 30 25 26 19 39 170 172.5 182.5 151.5 173 157 201 160 181 164 168 152 160 42 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 77 78 Male Female Male Male Female Female Male Female Female Female Male Female Female Male Female Male Female Female Male Female Female Female Female Male Female Female Male Male Female Female Male Male Male Female Female Male Female 30.5 24.5 25.5 27.5 24 23.5 33.5 24.5 23 25 28 23.5 19 28 24 28 21 24.5 28 27 30 22 26 26 23 23 27 23 22.5 23.5 30.48 32 29 24.5 27.94 26.5 23.5 186 172.5 183 190.5 166 169 182.5 165 161.5 178 183 160 153 178 180 184 156 165 185.5 148 193 159 185 183 165 162.5 168 173 164 160 183 185.5 184 155 171.5 179.5 165 33 24 19 21 37 32 27 32 26 34 39 29 25 27 21 28 23 20 26 40 19 31 45 29 27 26 29 40 22 19 21 41 27 41 41 25 26 190.5 172.5 177 191.5 176 167.5 181.5 171 163 170 190.5 162 194 180 180 185.5 168 165 201 152 193 159 169 179 164 162.5 175 160 160 155 178 180.5 186 154 170.18 184.5 160 udent Data Number in Family Hair Color 4 10 1 6 5 5 3 5 3 8 3 4 Blonde Brown Blonde Brown Black Blonde Black Brown Brown Brown Brown Brown 5 4 3 1 5 5 5 Brown Brown Brown Brown Red Brown Brown 4 4 3 9 1 2 4 Brown Brown Blonde Black Brown Brown Brown 3 Red 4 3 8 4 4 5 2 3 3 3 4 4 4 Red Brown Brown Red Brown Blonde Brown Brown Brown Blonde Brown Brown Blonde 7 6 5 12 4 5 3 6 12 4 4 6 4 5 4 1 3 9 7 4 3 4 4 3 5 2 4 5 4 3 3 6 4 4 6 7 4 Brown Brown Blonde Brown Brown Brown Brown Blonde Brown Brown Brown Brown Blonde Black Blonde Brown Blonde Brown Blonde Black Blonde Blonde Blonde Brown Blonde Red Black Black Blonde Blonde Blonde Blonde Blonde Brown Brown Black Brown