Answer to Question #161698 in Statistics and Probability for Qianzi

Question

An investor is considering six different money market funds. The average number of

days to maturity for each of these funds is as follows:

41 39 35 35 33 38

i. Construct a sampling distribution of sample mean with samples of size

five, which can be selected without replacement from this population.

ii. Find the sampling error for each sample.

iii. If Sally selected a sample of 5 numbers: 41, 39, 35, 33, 38 from this

population, and he recorded 28 instead of 38 for this sample, what is the

non-sampling error?

Answer 1

The Given sample of market funds are:-

41 , 39 , 35 , 35 , 33 , 38

We have to construct a sampling distribution of size 5 i.e. n=5

(i) Sampling Distribution is Given by-

The sampling distribution about the sample means is given in the table below:-

Mean about market funds is $\mu=\dfrac{41+39+35+35+33+38}{6}=36.83$

Variance is given by, $\sigma^2=\dfrac{0.0529+0.5929+0.1369+0.1369+0.43+0.6889}{6}=0.3408$

(ii) Sampling error for each sample is given by taking the difference between sample mean and the mean of given samples :-

and The difference are

$0.23, 0.77, -0.37, 0.43, 0.83$

Hence Sampling error for each sample is- $0.23, 0.77, -0.37, 0.43, 0.83$

(iii)When 28 is taken into the account

i.e. The sample set is 41, 39,35,33,28

Then sample mean 2 =$\dfrac{41+39+35+33+28}{5}=\dfrac{176}{5}=35.2$

And when 38 is taken into account

Then sample mean 1 is $37$

Then, Non-sampling error is given by=Sample mean 1-sample mean 2=$37-35=2$

Hence Non-sampling error is 2.