Question

Data from a recent year showed that 73% of the tens of thousands of applicants to a certain program were accepted. A company that trains applicants claimed that 207 of the 250 students it trained that year were accepted. Assume these trainees were representative of the population of applicants. Has the company demonstrated a real improvement over the​ average? Complete parts a through c below. Assume the independence assumption is met.

What is the​ P-value?

Answer 1

n = 250, x = 207  

p̄ = x/n = 0.828  

Null and Alternative hypothesis:

Ho : p = 0.73  

H1 : p > 0.73  

Test statistic:   

z =(p̄ -p)/(√(p*(1-p)/n)) = 3.4902

P-value = 1- NORM.S.DIST(3.4902,1 ) = 0.0002

Decision:   

p-value < α, Reject the null hypothesis.