3. You measure a quantity four times and the standard deviation is 1.0%of the av

Question

3. You measure a quantity four times and the standard deviation is 1.0%of the average (a) Can you be at least 90% confident that the true value is within 1.2% of the measured average? (b) Can you be at least 95% confident that the true value is within 1.2% of the measure average?

4. It is found from a reliable assay that the ATP content of a certain type of cell is 111m mol/100 ml. You have developed a new assay, which gave the following values: 117, 119, 111, 115, 120 m mol/100 ml. The average value is 1164 m mol/100 ml. Can you be 95% confident that your method produces a result different from the “known value? Can you be 99% confident?

Explanation / Answer

3.

Standard deviation = 0.01* average

Standard error of mean = Standard deviation / sqrt(4) = 0.01* average / 2

(a)

Z value of 90% confidence interval = 1.64

Margin of error of 90% confidence interval = 1.64 *  0.01* average / 2 = 0.0082 = 0.82%

So, we are 90% confident that the true value is within 0.82% of the measured average. Therefore, we are atleast 90% confident that the true value is within 1.2% of the measured average

(b)

Z value of 95% confidence interval = 1.96

Margin of error of 95% confidence interval = 1.96 *  0.01* average / 2 = 0.0098 = 0.98%

So, we are 95% confident that the true value is within 0.98% of the measured average. Therefore, we are atleast 95% confident that the true value is within 1.2% of the measured average

4.

The average of new assay is 116.4 m mol / 100 ml

Standard deviation of samples 117, 119, 111, 115, 120 is 3.58

Standard error of mean = SD / sqrt(n) = 3.58 / sqrt(5) = 1.6

Z score for 95% confidence is 1.96

95% confidence interval is

(116.4 - 1.96 * 1.6, 116.4 + 1.96 * 1.6)

(113.264, 119.536)

As, 95% confidence interval does not contains the population average of 111m mol/100 ml, we are 95% confident that the method produces a result different from the “known value.

Z score for 99% confidence is 2.58

99% confidence interval is

(116.4 - 2.58 * 1.6, 116.4 + 2.58 * 1.6)

(112.272, 120.528)

As, 99% confidence interval does not contains the population average of 111m mol/100 ml, we are 99% confident that the method produces a result different from the “known value.

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