I have two following questions I could not really decipher how to get the P-Value.

Data from a recent year showed that 71% of the tens of thousands of applicants to a certain program were accepted. A company that trains applicants claimed that 163 of the 210 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?

I know that: Null Hyp. H0:p = 0.71 & HA: p>0.71

Independence, randomization, success/failure cond. & 10% cond are met.

I calculated the P-value by getting the proportion, then the SD(p hat) and then the z-score (0.21) to get the value that led me to a p-value of .5832. But this is waaaaay off...

Does anyone know how to calculate this with a graphing calculator? And could you explain me right right approach?


  • $\begingroup$ Why can't you use just R to do it? This is only a few lines in R.... Or you want a script that does it in R? There're tons of examples like that for R on Google. $\endgroup$
    – SmallChess
    Apr 14, 2015 at 6:14
  • $\begingroup$ Sorry... I only know Java, Python and C. Never used R in my life $\endgroup$
    – user73495
    Apr 14, 2015 at 6:27
  • $\begingroup$ I know its a prog lang for stats tho. BTW, how is it? $\endgroup$
    – user73495
    Apr 14, 2015 at 6:27
  • $\begingroup$ If you're a programmer, you should learn to use R. Doing it in the traditional language require lots of stuffs like getting the underlying distribution to work. However, I'm sure there is a python package for it. Google. $\endgroup$
    – SmallChess
    Apr 14, 2015 at 6:30
  • $\begingroup$ I'll keep that in mind! Thanks for the useful info $\endgroup$
    – user73495
    Apr 14, 2015 at 6:37

1 Answer 1


you did something wrong.

Let us say Acceptance follows Binomial distribution.and as acceptance is discrete you'd check >=162.5/210

Now, $$\bar{X}\sim N(0.71,0.71*0.29/210)$$ So $$Z=\frac{\frac{162.5}{210}-0.71}{\sqrt{\frac{0.71*0.29}{210}}}=2.0378$$(with continuity correction)

or $$Z=\frac{\frac{163}{210}-0.71}{\sqrt{\frac{0.71*0.29}{210}}}=2.11386$$(without continuity correction)

therefore, P-value=0.0208(with continuity correction) P-value=0.01726(without continuity correction)

  • $\begingroup$ the correct answer is 0.0173 :( $\endgroup$
    – user73495
    Apr 14, 2015 at 6:38
  • $\begingroup$ I dont know how to get to it though $\endgroup$
    – user73495
    Apr 14, 2015 at 6:38
  • $\begingroup$ I used central limit theorem for mean $\endgroup$ Apr 14, 2015 at 6:45
  • $\begingroup$ usablestats.com/lessons/central_limit see $\endgroup$ Apr 14, 2015 at 6:45
  • 4
    $\begingroup$ Please don't give complete answers to homework. Hints and guidance are okay. $\endgroup$
    – Glen_b
    Apr 14, 2015 at 10:42

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