Final answer:
To determine if the mean age of employees is more than 41 years using the p-value approach, set up null and alternative hypotheses, perform a statistical test to obtain a p-value, compare it with the level of significance, and then accept or reject the null hypothesis based on this comparison.
Step-by-step explanation:
To determine whether or not the mean age of all employees is significantly more than 41 years using the p-value approach, we start by setting up our null hypothesis (H0) and our alternative hypothesis (Ha). The null hypothesis would state that the mean age is 41 years or less (H0: μ ≤ 41), while the alternative hypothesis states that the mean age is more than 41 years (Ha: μ > 41).
After collecting sample data, we would perform a statistical test such as a t-test or a z-test, depending on the sample size and whether the population standard deviation is known. The test would generate a p-value, which represents the probability of observing a sample mean as extreme as the one measured (or more extreme) if the null hypothesis were true.
If our calculated p-value is less than our chosen level of significance (also known as alpha, α), it suggests that such an extreme result would be unlikely under the null hypothesis, so we reject H0 in favor of Ha. Conversely, if the p-value is greater than α, we do not reject H0.
For example, if our p-value is 0.03 and α is set to 0.05, we would reject the null hypothesis since 0.03 < 0.05, concluding that there is sufficient evidence to say the mean age is more than 41. However, if α were set to 0.01, we would not reject the null hypothesis, as 0.03 > 0.01, indicating insufficient evidence at the 1 percent level to suggest the mean age is more than 41.