Problem 2: Iron Maiden Song Length (there is no data file for this problem) In 1982, the heavy metal band Iron Maiden introduced their new singer Bruce Dickinson on the release of their third album. Dickinson would sing on seven studio albums from 1982 to his departure from the band in 1992. Dickinson later rejoined the group in 2000 and has since sung on the five studio albums released since that point. A statistician wishes to investigate whether or not the length of songs on studio albums differed during Dickinson's two tenures with the band. A random sample of songs was taken from each of the two periods and the mean and standard deviation of the samples were found in the table below. You may assume all conditions that allow for inference using the t-distribution are met. Before (1982-92) After (2000-16) Sample size, n 16 songs 13 songs Sample mean, x 5.20 min 7.70 min Sample standard deviation, $ 1.24 min 3.45 min a) State the hypotheses you would use to test the claim that a significant difference exists in the average song length between the two periods of the band. b) Define the population parameter you stated in the hypotheses in context of this question in one sentence