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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? Explain.

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jmonterrozar

Answer:

The requirements for the hypothesis test are not met

Step-by-step explanation:

We have the following information from the statement:

sample size = n = 60

Probability = p = 13% = 0.13

Now, we calculate the multiplication of this which would be:

n * p = 60 * (0.13) = 7.8 which is less than 10

Therefore the requirements for the hypothesis test are not met, since the multiplication of n by p would have to be greater than 10 for it to be met, but this is not the case.

Since [tex]np = 7.8 < 10[/tex], the requirements for the hypothesis test were not met.

The requirements for an hypothesis test involving a proportion p in a sample of size n is that there are at least 10 successes and 10 failures in the sample, that is:

[tex]np \geq 10[/tex]

[tex]n(1 - p) \geq 10[/tex]

In this problem:

  • Proportion of 13% tested, hence [tex]p = 0.13[/tex]
  • Sample of 60, hence [tex]n = 60[/tex]

Then:

[tex]np = 60(0.13) = 7.8 < 10[/tex]

Since [tex]np = 7.8 < 10[/tex], the requirements for the hypothesis test were not met.

A similar problem is given at https://brainly.com/question/24261244