Question

(20 points) A study is being conducted on the average human body temperature under normal conditions. The study obtained the following data in fahrenheit. Men 96.9 97.4 97.5 97.8 97.8 | 97.9 98 98.1 98.6 98.8 97.2 99.1 98.3 96.9 97.5 T T T Women 97.8 98 98.2 98.2 98.2 98. 6 98.8 | 98.8 | 99.2 99.4 98.2 97 | 97.3 98.9 97.9 99.1 (a) Treating this data as a simple random sample, estimate the average body temperature and place a bound on the error of estimation. Is there evidence to suggest the average body temperature is different from the accepted value of 98.6? (5 points) (b) The researchers postulated that men and women might have different average body tempreatures, so they also recorded the gender of each person sampled. Treating the above a stratified random sample, estimate the average body temperature and place a bound on the error of estimation. Is there evidence to suggest the average body temperature is different from the accepted value of 98.6? (7 points) (c) Does treating the sample as stratified improve our estimation of the average body temperature? Explain. (3 points) (d) Estimate the difference in men and women's average body temperature. Is there evidence to suggest that men and women indeed have different average body temperatures? (5 points)

Answer 1

Solution Coveo chlo (a) "Ticalingil os Soropte rondbro bio u tovo obarvalion or th both men and unwon togethey average buty temperaturo (10) Cum of all Obervations ber rron and women Ino ol (men turoweo) = 2041 4 131 : 9% for Error Oľ Ellimolion onore cokius or calculate Standard deviation Standard deviation : 6:1 Ñ ? (X-M)! = 0:688 Standard Error : 01 SqrtN): 0.124 bound on Error al estimation associated cuilh a confidence interval is: (7 critical value ). (Standard Enyor ol the Statistic). for 967. confidence interval Bound on Envoy of Estimation is : 196 x 0.124 - 10.249 01 +0.251. Accovoding to observation Averago Bosiy temperature is different from acceptable value.

(b) Con Sickring it as Stralified foropi pare con mon and men sparately for calculation first tuv Sliala Pen med are moon and common amarengo Average Temperature for men m = Surn d all over I no. of men E9185 (C) average temperature for womeo 149835 E Nath tolal averag 5 = π h h ah Where di number of sirata No the sum of all stratum hos sizes Np - Size of Straturoh in- Sample man al Stralumh n = number of observation on Stratum h She Sample Standard deviation of Stratum h =98.11 Same as when we took it as sample random data Similarly for women for as.. Confidence interval Bound on error of Estimation is = 1.96 -* 0.1629 = 10.319 or 10:32:2.

for men for 95% confidence confidence interval Bound on . tistimation Error of is = 1.96 x 0.1632 = oto:32 OY = id) difference is 0.5 degree t 0.3.3% in both genders celsius. average temperatu Thank you give me thumb.