Chapter 4: QFE (page 90)

A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is. You developed a new assay, which gave the values117,119,111, 115, 120 $μ m o l / 100 m L$ (average = 116.4) for replicate analyses. Do your results agree with the known value at the 95%confidence level?

Short Answer

Expert verified

The 95% confidence interval does not include the accepted value of $111 μ m o l / 100 m L$

Step by step solution

Definition of standard deviation and mean.

Arithmetic mean: By dividing the amount of measured values by the number of measurements , the arithmetic mean $\bar{x}$ is determined.

Mean:

Standard deviation: The standard deviation is a measurement of how tightly the data cluster around the mean.

The standard deviation (s) is given by the formula:

$s = \sqrt{\frac{\sum_{i} {(x_{i} - \bar{x})}^{2}}{n - 1}}$

Standard deviation of the mean of sets of n values is:

$σ_{n} = \frac{θ}{\sqrt{n}}$

Explanation.

The mean:

$\bar{x} = \frac{\sum_{i} x_{i}}{n} = \frac{117 + 119 + 111 + 115 + 120}{5} = 116.4 = 116 (r o u n d e d o f f)$

Standard deviation:

$s = \sqrt{\frac{\sum_{} {(x_{i} - \bar{x})}^{2}}{n - 1}} = \sqrt{\frac{{(116 - 117)}^{2} + . . . . . + {(116 - 120)}^{2}}{(5 - 1)}} = 3.58 = 4 (r o u n d e d o f f)$

95% Confidence interval:

The 95% confidence interval for four degrees of freedom is calculated as follows,

Confidence interval $= \bar{x} \pm \frac{t s}{\sqrt{n}}$

$= 116.4 \pm \frac{(2.776) (3.58)}{\sqrt{5}} = 116.4 \pm 4.4 = 116 \pm 4 (r o u n d e d o f f) = 112.0$

or 120.8 (digits in subscript denotes insignificant figures)

The 95% confidence interval does not include the accepted value of $111 μ m o l / 100 m L$ Hence, the difference is significant.

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A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is. You developed a new assay, which gave the values117,119,111, 115, 120 $μ m o l / 100 m L$ (average = 116.4) for replicate analyses. Do your results agree with the known value at the 95%confidence level?

Short Answer

Step by step solution

Definition of standard deviation and mean.

Explanation.

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A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is. You developed a new assay, which gave the values117,119,111, 115, 120μmol/100mL(average = 116.4) for replicate analyses. Do your results agree with the known value at the 95%confidence level?

Short Answer

Step by step solution

Definition of standard deviation and mean.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Organic Chemistry

Chemical Analysis

Chemistry Branches

The Earths Atmosphere

Chemical Reactions

Study anywhere. Anytime. Across all devices.

A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is. You developed a new assay, which gave the values117,119,111, 115, 120 $μ m o l / 100 m L$ (average = 116.4) for replicate analyses. Do your results agree with the known value at the 95%confidence level?