Final answer:
The student's question involves hypothesis testing in statistics at the College level, specifically conducting a one-sample z-test to determine if there is a significant difference between a sample mean and a known population mean.
Step-by-step explanation:
Hypothesis Testing in Statistics
The subject of this question is statistics, a branch of mathematics. The student is dealing with hypothesis testing which is used to determine whether a statistical hypothesis about a population parameter should be rejected or not. In hypothesis testing, we have a null hypothesis (H0), which is a statement about a population parameter that we assume to be true until we have enough evidence against it, and an alternative hypothesis (Ha), which is a statement that contradicts the null hypothesis and is what we suspect might be true instead.
The student's question pertains to a one-sample z-test since the population variance is known. Here's a step-by-step explanation for such a statistical test:
- State the null hypothesis H0: μ = 47 and the alternative hypothesis Ha: μ ≠ 47.
- Choose a significance level (α), typically 0.05. The significance level is the probability of rejecting the null hypothesis when it is actually true.
- Calculate the test statistic based on the sample data.
- Determine the p-value, which is the probability of observing a test statistic as extreme as, or more extreme than, the sample result if the null hypothesis were true.
- Compare the p-value to the chosen α. If the p-value is less than α, reject the null hypothesis.
- Based on the decision, conclude whether or not there is sufficient evidence to support the claim that the population mean is significantly different from 47.
For example, if a sample has a mean significantly greater than the hypothesized population mean, with a p-value smaller than the significance level, you would reject the null hypothesis, indicating that there is evidence to suggest the population mean is indeed different from 47.