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Testing a Claim about Mean: Unknown Population SD01:21

Testing a Claim about Mean: Unknown Population SD

A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Cancers Originate from Somatic Mutations in a Single Cell02:21

Cancers Originate from Somatic Mutations in a Single Cell

Cancer arises from mutations in the critical genes that allow healthy cells to escape cell cycle regulation and acquire the ability to proliferate indefinitely. Though originating from a single mutation event in one of the originator cells, cancer progresses when the mutant cell lines continue to gain more and more mutations, and finally, become malignant. For example, chronic myelogenous leukemia (CML) develops initially as a non-lethal increase in white blood cells, which progressively...
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Induced Pluripotent Stem Cells01:13

Induced Pluripotent Stem Cells

Stem cells are undifferentiated cells that divide and produce different types of cells. Ordinarily, cells that have differentiated into a specific cell type are post-mitotic—that is, they no longer divide. However, scientists have found a way to reprogram these mature cells so that they “de-differentiate” and return to an unspecialized, proliferative state. These cells are also pluripotent like embryonic stem cells—able to produce all cell types—and are therefore...
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Induced-fit Model01:13

Induced-fit Model

Most chemical reactions in cells require enzymes—biological catalysts that speed up the reaction without being consumed or permanently changed. They reduce the activation energy needed to convert the reactants into products. Enzymes are proteins, that usually work by binding to a substrate—a reactant molecule that they act upon.
Enzymes exhibit substrate specificity, meaning that they can only bind to certain substrates. This is mainly determined by the shape and chemical...
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Induced Electric Dipoles01:28

Induced Electric Dipoles

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...
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