Statistics
xb_sama1
exam_ii.docx
Q2 – The following table shows the stratification of all farms in a county by farm size and mean and variance of the number of acres of corn in each stratum
|
Farm size |
Ni |
i |
i2 |
|
1 – 80 |
500 |
26.3 |
400 |
|
81 – 160 |
300 |
44.3 |
576 |
|
161 – 240 |
150 |
102.1 |
625 |
|
241 + |
150 |
163.8 |
1024 |
a) For a sample of 100 farms, compute the sample sizes according to optimal allocation
b) Calculate the variance of the sample mean for the above sample (in a)
c) If 25 farms are sampled from each farm size group, what would be the variance for the sample mean?
Q3 – Suppose X1, X2, …, Xn are i.i.d. random variables from a distribution where E(X) = 1/3 and Var(X) = 2/[9(3 + 1)] where > 0. How would you find estimator of using the method of moments?
Q4 – A sample of 110 observations provided the following frequency distribution table.
If one of the researchers claimed that this comes from normal population with mean = 16.5 and standard deviation = 3.0. Is he right?
Q5 – Hampton & Walker made measurements of the heats of sublimation of rhodium. Do the following calculations for each of the two given data sets:
Rhodium:
|
126.4 |
133.3 |
131.3 |
134.2 |
|
135.7 |
132.5 |
131.2 |
133.8 |
|
132.9 |
133 |
132.1 |
133.3 |
|
131.5 |
133 |
131.1 |
133.5 |
|
131.1 |
132.4 |
131.4 |
133.4 |
|
131.1 |
131.6 |
131.2 |
133.5 |
|
131.9 |
132.6 |
131.1 |
133 |
|
132.7 |
132.2 |
131.1 |
132.8 |
a) Create a histogram, a stem & leaf plot and a boxplot
b) Find mean, 10% and 20% trimmed mean
c) Comment on your stem& leaf display
LowerMidpointUpperObserved
Low10128
1213.51526
1516.51845
1819.52122
2125High9
