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Determination of sodium level in separate portions of a blood sample by ion-selective electrode measurement gave the following results (meq/l): 139.2, 139.8, 140.1, 139.4 what is the range within which the true value falls at 95% confidence level? (t = 3.182) a) 139.30 to 139.95 b) 138.98 to 140.27 c) 137.20 to 141.39 d) 136.57 to 142.19
Accepted Answer
The range within which the true value falls at 95% confidence level is calculated using the formula:
Mean ± (t
Standard Deviation / √n)
Where:
Mean is the average of the measurements.
t is the t-value for the desired confidence level (95% in this case) and degrees of freedom (n-1).
Standard Deviation is a measure of the spread of the data.
n is the number of measurements.
In this case:
Mean = (139.2 + 139.8 + 140.1 + 139.4) / 4 = 139.625
t = 3.182 (given)
Standard Deviation = 0.349 (calculated from the data)
n = 4
Therefore, the range is:
139.625 ± (3.182
0.349 / √4) = 139.625 ± 0.555
This gives a range of 139.07 to 140.18.
The closest option is B) 138.98 to 140.27. This may be due to rounding in the calculations.
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