BIOT 6214 Assignment #3

BIOT 6214 NAME _____________________ Assignment #3 5 points 1. (1 point) Our sample size is n=36 for a quality of life (QoL) measurement from a population with a normal distribution with  =12 and  =6. a) What is the expected mean and the standard error for a sample size of n=36? =AVERAGE(A3:A38) 0.9857602778 12/sqrt(36)=SE =2 b) What is the probability that the sample mean will be greater than 13? =NORMDIST(13,0.9857602778,6,TRUE) 98.5% 2. (1 point) We now take a sample of size n=25 for a quality of life (QoL) measurement from a population with a normal distribution with  =9 and  =6. a) What is the expected mean and standard error for a sample size of n=25? Mean =9 =6/SQRT(25) SE = 1.2 b) What is the probability that the sample mean will be less than 10? =NORM.DIST(10,12,6,TRUE) 0.3694413402 = 36.9% 3. (1 point) A sample of size n = 114 produced the sample mean of m = 19. Assuming the population standard deviation σ = 7, compute a 95% confidence interval for the mean m. = 7 /SQRT( 114 ) =SE =( 0.6556100681 ) =19+(2*0.6556100681) =19-(2*0.6556100681) {17.68877986, 20.31122014 } 4. (1 point) Assuming the population standard deviation σ = 3, how large should a sample size be to estimate the population mean µ with margin of error not exceeding 0.4? (With 95% confidence.) 216.09 = 216 =((1.96^2)(3^2))/(0.4^2) =(3.8416*9)/0.16 5. (1 point) To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1.00 gram is repeatedly weighed 36 times. The resulting measurements (in grams) are shown to the right. Assume that the measured values are normally distributed. Use these data to compute a 95% confidence interval of the mean. SE= =0.05116801947/SQRT(36) = 0.008528003245 =0.9857602778+(2* 0.008528003245 )/(SQRT(36)) =0.9857602778-(2* 0.008528003245 )/(SQRT(36)) { 0.98 ,0.99} Question 5 Data weight(g) 0.942979 0.9985 1.020818 1.040727 1.011207 0.968857 1.027251 0.953533 0.986898 0.976004 1.047735 0.958451 1.007717 0.880931 1.102071 0.962264 0.985708 0.88476 0.965137 1.028819 0.962748 1.047765 0.907684 0.9474 1.049368 1.033281 0.96526 0.989381 1.06484 0.887259 0.942749 1.014474 0.958725 1.011039 0.968325 0.986705