According to a survey by the College Board, undergraduate students at private nonprofit four-year colleges spent an average of $1244 on books and supplies in 2014–2015 (www.collegeboard.org). A recent random sample of 200 undergraduate college students from a large private nonprofit four-year college showed that they spent an average of $1204 on books and supplies during the last academic year. Assume that the standard deviation of annual expenditures on books and supplies by all such students at this college is $200.

a. Find the p-value for the test of hypothesis with the alternative hypothesis that the annual mean expenditure by all such students at this college is less than $1244. Based on this p-value, would you reject the null hypothesis if the significance level is .025?
b. Test the hypothesis of part a using the critical-value approach and α = .025. Would you reject the null hypothesis? Explain.