Final Answer:
To test μ versus μ₀, a random sample of size (n) is obtained from a population known to be normally distributed.
Step-by-step explanation:
In hypothesis testing, the comparison of a sample mean to a hypothesized population mean involves statistical techniques to draw conclusions about the population parameter. To test μ versus μ₀, where μ is the population mean and μ₀ is the hypothesized mean, we employ a hypothesis test for the mean. This involves calculating a test statistic based on the sample data and comparing it to a critical value or p-value.
Firstly, we compute the sample mean \(\bar{x}\) and the standard deviation \(s\) of the sample. Using these values, we calculate the test statistic \(t\) using the formula \(t = \frac{{\bar{x} - μ₀}}{{\frac{s}{\sqrt{n}}}}\), where \(n\) is the sample size. This test statistic follows a t-distribution with \(n-1\) degrees of freedom. We then compare \(t\) to the critical value or use it to find the p-value. If the p-value is less than the significance level (commonly 0.05), we reject the null hypothesis in favor of the alternative.
In summary, hypothesis testing for comparing a sample mean to a hypothesized population mean involves calculating a test statistic based on sample data, interpreting it in the context of a probability distribution, and making a decision about the null hypothesis. This process provides a rigorous and systematic approach to inferential statistics, allowing researchers to draw meaningful conclusions about population parameters.