Question

Explain why the statement \(\bar{x}=50\) is not a legitimate hypothesis.

Short answer

\(\bar{x}=50\) is not a credible hypothesis since it refers to a sample mean. Hypotheses should be made about population parameters. The correct hypothesis could be \(\mu=50\), where \(\mu\) signifies the population mean.

Step-by-step solution

Understanding hypotheses

A legitimate hypothesis in statistics must be a testable claim about a population parameter, such as the population mean (\(\mu\)), the population proportion (p), the population standard deviation (\(\sigma\)), among others.

Wrong reference

\(\bar{x}=50\) is not a legitimate hypothesis as it is a statement about a sample mean, not a population parameter. A sample mean is subject to variability and depends on the specific sample chosen.

Right reference

If you want to make a legitimate hypothesis, it should instead refer to a population parameter. For example, a correct hypothesis could be \(\mu=50\), where \(\mu\) represents the population mean.