0.01 G Scales
stats help please! :] multiple choice?
2.An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean μ and standard deviation σ = 10 bushels per acre.
Reference: Ref 6-2
If the average yield for these 25 plots is = 150 bushels per acre what is a 90% confidence interval for μ?
A.150 ± 3.92
B.150 ± 3.29
C.150 ± 0.784
D.150 ± 2.00
To assess the accuracy of a laboratory scale, a standard weight that is known to weigh exactly 1 gram is repeatedly weighed a total of n times and the mean is computed. Suppose the scale readings are Normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error no larger than ± 0.0001?
A.n = 10000
B.n = 100
C.n = 196
D.n = 38416
1) Answer to the question is (B) as detailed below
Sample size = n = 25
Standard deviation = 10
Sample mean = 150
Critical value for 90% confidence interval = 1.645
Standard error of Mean = S.D/sq rt n
= 10/sq rt 25
=10/5 = 2
90% confidence interval for mu = 150 +/- 1.645*2
= 150 +/- 3.29
2) Answer to the question is (D) as detailed below
Standard deviation = 0.01
Critical value for 95% confidence interval = 1.96
Margin of error = 0.0001
Margin of error = Critical value*Standard error
Standard error = Margin of error/Critical value
= 0.0001/1.96 = 0.000051
Another formula for Standard error = S.D/sq rt n
sq rt n = S.D/S.E
= 0.01/0.000051
= 196
n = 196^2 = 38416
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