Problem 1 The following sampling data for concentrations of benzene are given in
ID: 3207059 • Letter: P
Question
Problem 1
The following sampling data for concentrations of benzene are given in micrograms per liter.
1. Calculate the following statistical parameters for the log-transformed " raw data"
A. Mean, Xgm
B. Standard deviation
C. 95% Confidence limits
SAMPLE EVENT
Raw Data Concentration, X
Log transformed data
Y = ln(X)
1
0.059
-2.830
2
0.156
-1.858
3
0.185
-1.687
4
1.300
0.262
5
0.091
-2.397
6
0.048
-3.037
7
0.139
-1.973
8
0.56
-0.580
SAMPLE EVENT
Raw Data Concentration, X
Log transformed data
Y = ln(X)
1
0.059
-2.830
2
0.156
-1.858
3
0.185
-1.687
4
1.300
0.262
5
0.091
-2.397
6
0.048
-3.037
7
0.139
-1.973
8
0.56
-0.580
Explanation / Answer
x
-2.83
-1.858
-1.687
0.262
-2.397
-3.037
-1.973
-0.58
Sample mean (x bar) = S x / n = -14.1 / 8 = -1.7625
Sample Standard deviation (s) = Ö[ S(x – x bar)^2 / (n-1) ] = Ö8.7225/7 = 1.1163
Confidence Interval:
x bar (-/+) E
E = tc * ( s / sqrt (n))
tc is the critical value from t-table for 7 degrees of freedom at 5% level of significance.
tc = 2.365
E = 2.365 * ( 1.1163 / Ö8)
= 0.9334
x bar (-/+) E
-1.7625 (-/+) 0.9334
-2.6959 to -0.8291
Answers:
( A ) -1.7625
( B ) 1.1163
( C ) The 95% confidence interval is (-2.6959 to -0.8291)
x
-2.83
-1.858
-1.687
0.262
-2.397
-3.037
-1.973
-0.58
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