Final Answer:
The null hypothesis for the research hypothesis that weights are higher in 2015 than in 2012 would be: μ2015 ≤ μ2012.
Step-by-step explanation:
The null hypothesis (H₀) typically represents the status quo or a statement of no effect, change, or difference in a statistical test. In this scenario, if the investigator believes that weights increased from 2012 to 2015, the null hypothesis assumes that there is no increase or that weights in 2015 are less than or equal to the weights in 2012.
The notation "μ2015 ≤ μ2012" states that the population mean weight of women in 2015 (μ2015) is less than or equal to the population mean weight in 2012 (μ2012). This formulation suggests that any observed difference in weights between the two years would be due to chance variation rather than a genuine increase in weights.
When conducting hypothesis testing, researchers aim to gather evidence against the null hypothesis to support the alternative hypothesis (H₁), which in this case would suggest that the mean weight of women in 2015 is greater than the mean weight in 2012 (μ2015 > μ2012). This comparison helps determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a significant increase in weights between the two time periods.