2)Let D be the difference between two different measurements of pH. What is the
ID: 2930370 • Letter: 2
Question
2)Let D be the difference between two different measurements of pH.
What is the expected value and the standard deviation of D?
Remember that D can be both negative and positive!
3)What is the probability that the difference D should be greater than 0.01?
That is, what is the probability that two measurements will differ more than 0.01 from each other?
Remember that D can be both negative and positive!
4)you have taken four samples from the solution and found these four values: 7.58, 7.49, 7.62 and 7.55
Find a estimate point of the X value estimate:
and find a 95% confidence interval for [blank,blank]:
On the basis of the results you found, do you think the true pH value to be 7.50, or
would you doubt it?
5)How many measurements must we make at least to ensure that the confidence interval does not exceed 0.05?
Explanation / Answer
Solution4:
you have taken four samples from the solution and found these four values: 7.58, 7.49, 7.62 and 7.55
Find a estimate point of the X value estimate:
sample mean=sum/total
=7.58+7.49+7.62+7.55/4
=30.24/4
=7.56
estimate point of the X value estimate=7.56
sd=0.054772
t
95% confidence interval for mean=
samplemean-tcrit(samplesd/sqrt(n),samplemean+tcrit(samplesd/sqrt(n)
t crit fro 3df and 0.025 level of significance=3.182
7.56-3.182(0.055)/sqrt(4),7.56+3.182(0.055)/sqrt(4)
7.47,7.65
lower limit=7.47
upper limit=7.65
we are 95% confident that the true pH value lies in between 7.47 and 7.65
On the basis of the results you found, we think the true pH value to be 7.50 as it lies in the confidence interval range
X XBAR X-XBAR (X-XBAR)^2 7.58 7.56 0.02 0.0004 7.49 7.56 -0.07 0.0049 7.62 7.56 0.06 0.0036 7.55 7.56 -0.01 1E-04 MEAN=7.56 0.009 0.054772 variance=0.009/4-1 variance=0.009/3 variance=0.003 sd=sqrt(variance) sd=sqrt(0.003)sd=0.054772
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