Solved – Help with HW questions

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?


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)

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