The entrance rate into a prestigious university\'s graduate program is 13%. A st

Question

The entrance rate into a prestigious university's graduate program is 13%. A statistics student wants to know if the entrance rate of applicants from BYU-Idaho is greater than the typical entrance rate. He decides to conduct a hypothesis test of one proportion to determine whether the entrance rate of BYU-Idaho students into the graduate program is higher than 13%. He randomly selects 60 students who have applied and records whether or not each student was admitted. Were the requirements for the hypothesis test met?
A) Yes. There were more than 5 measurements.
B) Yes. There were more than 30 measurements.
C) Yes. np10 and n(1p)10.
D) Yes. Sample proportions always follow a normal distribution.
E) No. np<10.
F) No. np<10. No. n(1p)<10.
G) No. Sample proportions never follow a normal distribution.

Explanation / Answer

We know sample proportion follows Normal distribution when the number of observations / measurements considered to determine the sample proportion is more than 30. Here the number of measurements = 60.

Hence, The number of measurements is more than 30. So the requirement of hypothesis in terms of distributional assumption has been met. So Option (B) is the correct choice. (Ans).

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