1. An engineer wants to measure the bias in a pH meter. She uses the meter to me
ID: 3207024 • Letter: 1
Question
1. An engineer wants to measure the bias in a pH meter. She uses the meter to measure the pH in 6 neutral substances and obtains pH readings of 7.01, 7.04, 6.97, 6.99, 7.04, and 7.07
a. Find the mean and standard deviation for the pH values (show your work).
b. Create a 95% confidence interval for the pH values read by this meter.
c. Explain in context what your confidence interval tells you about the pH values read by this meter.
d. The actual pH of the substances tested was 7. Does it seem there is evidence the pH meter is testing inaccurately?
Explanation / Answer
( a )
x
7.01
7.04
6.97
6.99
7.04
7.07
Total =
42.12
Sample mean (x bar) = 42.12 / 6 = 7.02
Mean = 7.02
Sample standard deviation (s) = Ö[S(x – x bar)^2 /(n-1)]
x
( x - x bar)
( x - x bar)^2
7.01
-0.01
0.0001
7.04
0.02
0.0004
6.97
-0.05
0.0025
6.99
-0.03
0.0009
7.04
0.02
0.0004
7.07
0.05
0.0025
Total =
0.0068
s = Ö(0.0068/5) = 0.0369
Standard deviation = 0.0369
( b )
Confidence Interval:
X bar (-/+) E
X bar = 7.02
E = tc * ( s / Ön)
tc is the critical value we find it from t-table for 5 degrees of freedom at 5% level of significance.
tc = 2.571
E = 2.571 * (0.0369/Ö6)
= 0.0387
X abr (-/+) E
7.02 (-/+)0.0387
6.98 and 7.06
The 95% confidence interval is (6.98 to 7.06)
( c )
Here we are 95% confident that the population mean of pH level will lie in between 6.98 and 7.06.
( d )
The pH level of 7 falls in between the obtained interval. No, it does not seem that the pH meter is testing inaccurately.
x
7.01
7.04
6.97
6.99
7.04
7.07
Total =
42.12
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