Final Answer:
The null hypothesis (H0) for the age difference between Best Actresses and Best Actors is given by option c. μd = 0.The correct option is c. μd = 0.
Step-by-step explanation:
The null hypothesis (H0) represents the assumption of no significant difference or effect. In this context, the null hypothesis states that there is no average age difference (μd) between Best Actresses and Best Actors. Mathematically, this is expressed as μd = 0.
The subscript "d" typically denotes the difference, and "μ" represents the population mean. Therefore, the null hypothesis implies that, on average, there is no age distinction between male and female winners in the Best Actor and Best Actress categories.
The null hypothesis is crucial in statistical hypothesis testing as it serves as the starting point for making comparisons. In this case, if the null hypothesis is rejected based on the collected data, it suggests that there is a statistically significant age difference between Best Actresses and Best Actors. On the other hand, if there is insufficient evidence to reject the null hypothesis, it implies that any observed age difference is likely due to random chance rather than a meaningful pattern.
Researchers and statisticians use hypothesis testing to draw conclusions about populations based on sample data. The choice of the null hypothesis is fundamental to this process, and in the context of age difference between Best Actresses and Best Actors, the null hypothesis asserts that there is, on average, no distinction in age.
The correct option is c. μd = 0.