Question

A reliable assay shows that ADP (adenosine triphosphate) content of a certain cell type is 115 umol/100mL. You developed a new assay, which gave the values 113, 114, 119, 125, 130 umol/100mL (standard deviation = 3.4 umol/100mL) for replicated analyses. Do your results agree with the known value at the 95% confidence level?

Answer 1

Consider

X : Content of a certain cell type.

mu: Mean content of a certain cell type

From the information

mu = 115 and sigma = 3.4

We have to test the hypothesis

Whether or not mean content of a certain cell type is 115 umol / 100mL.

i.e. Null Hypothesis -

against

Alternative Hypothesis- ( two-tailed test).

since population standard deviation is known, we use one sample z-test for testing population mean.

The value of test statistic is

Xbar =sum(X) / n = ( 113 +114 + 119 + 125 +130) / 5 =120.2

Value of test statistic Z = 3.4198.

Alpha: level of significance = 0.05

Since the value of test statistic is 3.4198 and test is two-tailed, p-value is obtained by

p-value = 2 * P ( Z >3.4198)

from normal probability table

P ( Z > 3.4198) = 0.0003

Hence p-value = 2 *0.0003 = 0.0006.

Decision : Since p-value < level of significance alpha, we reject Ho at 5% level of significance.

Conclusion: There is not enough sufficient evidence support to claim that mean content of a certain cell type is 115 umol / 100mL.