A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a sample of 26 elementary school teachers is $48,300, and the sample standard deviation is $3,912.40. The mean of the salaries of a sample of 25 secondary school teachers is $46,200. The standard deviation is $5,533. At a significance level of 0.10, can it be concluded that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers? Use the P-value method and use μ1 for the mean of the salaries for elementary school teachers. Assume the variables are normally distributed and the variances are unequal. State the hypotheses and identify the claim with the correct hypothesis.