Final answer:
The appropriate null hypothesis would state that there is no difference between the two populations, either as proportions or means. Therefore, the correct options would be 'p2011 = p2010' if comparing proportions or 'μ2011 = μ2010' if comparing means, since these null hypotheses suggest no change or difference across time.
Step-by-step explanation:
An appropriate null hypothesis generally posits that there is no effect or no difference and is used as a starting point for statistical testing. In the context where you are comparing two population proportions (p2011 and p2010) or two population means (μ2011 and μ2010), we want to construct a null hypothesis that reflects no change or difference between the two populations across time. The null hypothesis for comparing two population proportions would typically be stated as 'p2011 = p2010' which means there is no difference in the proportions from 2010 to 2011. Similarly, the null hypothesis for comparing two population means would be stated as 'μ2011 = μ2010' indicating that there is no difference in the means from 2010 to 2011. Therefore, the correct options for an appropriate null hypothesis are either a) 'p2011 = p2010' if p denotes proportion or c) 'μ2011 = μ2010' if μ denotes mean of the populations being compared. Option b) and d) would represent the alternative hypotheses, which are statements that there is a significant difference between the two proportions or means, respectively.