SOLUTION: Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year�s entire bin. The test statistic from the first

Question 138366: Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year�s entire bin. The test statistic from the first sample was 1.8, the test statistic from the second sample was 2.5, and the research team was astonished to learn that the mean and standard deviation were identical for both samples. If the first sample was composed of 16 kernels, how many kernels were weighed on the second occasion?

a. 8
b. 12
c. 22
d. 31

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year�s entire bin.
The test statistic from the first sample was 1.8, the test statistic from the second sample was 2.5, and the research team was astonished to learn that the mean and standard deviation were identical for both samples.
If the first sample was composed of 16 kernels, how many kernels were weighed on the second occasion?
a. 8
b. 12
c. 22
d. 31
--------------------
1st Sample test statistic:
t(x) = (x-u)/[s/sqrt(16)] = 1.8
x-u = (s/4)*1.8 = 0.45s
--------------------------------
2nd Sample test statistic:
t(x) = (x-u)/[s/sqrt(n)] = 2.5
x-u = s/sqrt(n)*2.5
-------------------------
Equation those two expressions for x-u you get
2.5s/sqrt(n) = 0.45s
sqrt(n) = 2.5/0.45 = 5.55555...
n = 31 (number in the 2nd Sample)
=======================
Cheers,
Stan H.
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