An education researcher claims that stipends for PhD students have increased from one academic year to the next. The table shows the PhD stipends (in dollars per academic year) for seven different fields of study at various institutions in two consecutive academic years. At α = 0.05, is there enough evidence to support the education researcher’s claim?

(a) Identify the claim and state H₀ and H_a, 

(b) Find the critical value(s) and identify the rejection region(s), 

(c) Calculate d and s_d, 

(d) Find the standardized test statistic t, 

(e) Decide whether to reject or fail to reject the null hypothesis, and 

(f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.

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Field of Study 2 3 4 5 Stipend (first year) 30,600 29,658 15,200 26,233 11,900 33,000 33,590 Stipend (second year) 19,800 30,770 32,850 27,100 11,000 33,000 30,312 2.