Question

 A rowing team consists of four rowers who weigh 152, 156, 160 and 164 pounds. 

 

1. How many samples of size n=2 can be drawn from this population ?
2. Construct a table showing all possible samples, mean and probability of each sample.
3. Construct the sampling distribution ( probability distribution ) of the sample means.
4. Draw the histogram of the sampling distribution of the means

Answer 1

1. $C^2_4=\frac{4!}{2!2!}=6$

2. m(152,156)=(152+156)/2=154

m(152,160)=(152+160)/2=156

m(152,164)=(152+164)/2=158

m(156,160)=(156+160)/2=158

m(156,164)=(156+164)/2=160

m(160,164)=(160+164)/2=162

3. Frequencies

F(154)=F(156)=F160)=F(162)=1

F(158)=2

Probabilities $P(x)=F(x)/\sum F(x)$

P(154)=P(156)=P(160)=P(162)=1/6

P(158)=2/6