According to a book published in 2011, 45% of the undergraduate students in the United States show almost no gain in learning in their first two years of college (Richard Arumet al., Academically Adrift,University of Chicago Press, Chicago, 2011). A recent sample of 1500 undergraduate students showed that this percentage is 37%. Can you reject the null hypothesis at a 2.5% significance level in favor of the alternative that the percentage of undergraduate students in the United States who show almost no gain in learning in their first two years of college is currently lower than 45%. Use both thep-value and the critical-value approaches.

Round your answers for the observed value ofzand the critical value ofzto two decimal places, and thep-value to four decimal places.

z_observed=

p-value

Critical value =

Hence we can conclude that the percentage of undergraduate students in the U.S. who show almost no gain in learning in their first two years of college is currently