In the quantitative analysis lab, a student analysis a sample of impure potassiu

Question

In the quantitative analysis lab, a student analysis a sample of impure potassium hydrogen phthalate (KHP) and reports a 22.58% KHP content in the sample as the mean of 3 replicate measurements and a standard deviation of 0.55 of % KHP. Tie manufacturer indicates the sample to be 24.02% KHP. Is there systematic error in the student measurement at 95% confidence level? The confidence interval for the student is 22.58 plusminuse 1.67 % KHP, the manufacturers value is within this range, B therefore there is not systematic error in the student measurements. The reason the values differ may be due to random error. The confidence interval for the student is 22.58 plusminuse 1.37 % KHP, the manufacturer's value is not within this range, therefore there is systematic error in the student measurements. The absolute error is larger than the statistical error (margin of error) at 95% confidence level, therefore there is systematic error in the student measurements. The calculated t-exp value is 4.535 which is larger than the t value reported in the t-table, the t-crit is 4.303. The B experimental error is larger than the statistical error due to random error, therefore there is bias in the student s measurement and this indicates the presence of systematic error. The calculated t-exp value is 3.703 which is smaller than the t value reported in the t-table, the t-crit is 4.303. The experimental error is less than the statistical error due to random error, therefore there is no bias in the student's measurement and this indicates the absence of systematic error. The reason the values differ may be due to random error. The absolute error is smaller than the statistical error (margin of error) at 95% confidence level, therefore there is not systematic error in the student measurements. The reason the values differ may be due to random error.

Explanation / Answer

For a 95% confidence interval, there will be a 95% probability that the true value lies within the range of the calculated confidence interval, if there are no systematic errors.

Hence Conficende intervel = mean value + (standard error X t)

where t is the value of the t statistic for the number of measurements averaged and the confidence interval desired.

here it is a three sample system, therefore degrees of freedom is 3-1=2

for 95% conficence data from the standard stastical data for a sample with 2 degrees of freedom t=4.30

therefore Conficende intervel = mean value + ((standard deviation / n0.5 )X t)

Conficende intervel = 22.58 + ((0.55 / 30.5 )X 4.30)= (22.58 + 1.37) %

Hence it is proved that as the confidence intervel for the student is 22.58 + 1.37 % KHP, themanufactures value is not with in the range. therefore there is a systamatic error in the student measurement.

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