Question

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 Arum et al., Academically Adrift, University of Chicago Press, Chicago, 2011). A recent sample of 1500 undergraduate students showed that this percentage is 38%. 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 the p-value and the critical-value approaches Round your answers for the observed value of z and the critical value of z to two decimal places, and the p-value to four decimal places. observed p-value Critical value- B 4596. 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

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.45
H_A : p < 0.45

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	570	1500	0.38	0.012845233	-5.4494926	<0.0001

Hence,

z_observed = -5.45

p - value = 0

Critical value = -1.96

Lower than