Question
Question 4: To access the accuracy of a laboratory scale, a standard weight known to weigh...
Question 4: To access the accuracy of a laboratory scale, a standard weight known to weigh 10g is weighed repeatedly. The scale readings are normally distributed with standard t. The weight is measured five times. The mean result is 0.0023g. Give a 91.64% b. How rnany measurements needed to get the bound on the error of estimation with 98% deviation 0.0002g confidence interval for the mean of the true weight. confidence is less than 0.0001?
Answers
SolutionA:
sample mean=10.0023g
n=5
alpha=1-0.9164=0.0836
given std deviation=0.0002 g
91.64 % confidence interval for mean is given by
xbar-margin of error and xbar+margin of error
margin of error in excel is
=CONFIDENCE.NORM(0.0836;0.0002;5)
=0.000155
91.64 % confidence interval for mean of true weight is given by
10.0023-0.000155 and 10.0023+0.000155
10.00215 and 10.00245
lower limit= 10.00215
upper limit=10.00245
Solutionb:
E=0.0001
z crit for 98%=2.326
n=(Z alpha/2*sigma/E)^2
=(2.326*0.0002/0.0001)^2
n=21.64
n=22
Required sample szie=n=22
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