All possible samples of size 15 were taken from a particular population. The mea
ID: 3361477 • Letter: A
Question
All possible samples of size 15 were taken from a particular population. The mean of all the sample means was found to be 25.3 and the variance of the sample means was 1.75 g2o ) [IIThe mean and standard deviation of the population are: 25.3, 1.323 b. 25.3, 5.123 c. 25.3, 6.78 d. impossible to determine the mean of the sample means and the variaace of sample means have been if the samples had been of size 80? ] When n 15, what must be true regarding the distribution of the population in order to compute probabilities regarding the sample mean? l] Assuming the requirements in part (ii) are satisfied, describe the shape of the sampling distribution of the mearn 2 marke) large freight elevator can transnort a maximum of 9800 pounds. Sunpose a load ofExplanation / Answer
Given
n=15,
E(Sample Mean) =mu = 25.3 and variance(sample mean) = sigma2/n=1.75
sigma2= 15*1.75= 26.25 Sigma= sqrt(26.25)=5.1234
The mean and standard deviation of population are 25.3 are 5.123
ii) n=80
E(Sample mean) =mu = 25.3 and variance(sample mean) =sigma2/n = 26.25/80 = 0.3281
The mean and variance of the sample mean if sample size 80 are 25.3 and 0.3281 respectively.
iii) Central limit theorem states that if you a population with mean mu and variance sigma 2 then the distribution sample mean is approximately normal. This will hold true regardless whether the source population is normal or skewed, provided the sample size is large (n>=30). If the population is normal the theorem is hold true even if the samples smaller tha n 30.
n=15
The distribution of population is X ~ N(mu,Sigma2) and the distribution of sample mean
Xbar ~ N (mu, Sigma2/n)
iv) Sampling distribution of mean is normal. The shape of the distribution of sample mean should bulge in the middle and taper at the ends with a shape that is somewhat normal.