Assume that Qatar University is going to install a new elevator for student use

Question

Assume that Qatar University is going to install a new elevator for student use in the new library building; so, it has to decide about it. For this purpose, the average weight of the student (mu) the university is needed as a statistician you are asked to stratify the students based on gender (female or male). Assume that the university consists of 20000 students of which 15500 are females. A stratified random sample of size n_1=60 females and n_2 = 20 males were taken. the average weight for females in sample was found to be 59.5 kg with sample standard deviation of 4.2 kg, while the average weight for males in the sample was found to be 67 kg with sample standard deviation of 6 kg. Estimate the average weight of the students in Qatar University (mu)and Place a bound on the error of your estimation. Also, give an approximate 95% C.I. for mu. If a stratified sample of size n = 100 is to be taken from the population and allocated using Nyman allocation, what will be the values of n_1 and n_2. what is required sample size n and (n_1, n_2)?

Explanation / Answer

a)

Avg Weight=60/80*59.5+20/80*67=44.625+16.75=61.375

Std Error=(1/20000)*sqrt{[15500^2*(1-60/15500)*(4.2)^2/60]+[4500^2*(1-20/4500)*(6)^2/20]}

               =0.51

Critical value of Z from the table is 1.96

Margin of error is 1.96*0.51=0.9996

Confidence interval is 61.375+-0.9996=60.3754 to 62.3746

b)

100*(15500*4.2)/[15500*4.2+4500*6]=100*(65100)/[65100+27000]=70.68=71 females and 29 males.

c)

Probability is 1/20000=0.00005

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