The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample 0f 300 persons to whom materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of significance, should we reject director’s claim?

Question

The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission.  In a sample 0f 300 persons to whom materials were sent, 30 students applied for admission.  In a two-tail test at the 0.05 level of significance, should we reject director’s claim?

MathGuru · Accepted Answer

Null hypothesis:
Ho: p = .15 -->meaning: population proportion is equal to .15
Alternative hypothesis:
Ha: p does not equal .15 -->meaning: population proportion is not equal to .15 (this is a two-tailed test because the alternative hypothesis doesn't specify a specific direction)

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = .10 - .15 -->test value (30/300 = .10) minus population value (.15)
divided by
√[(.15)(.85)/300] -->note: .85 is 1 - .15

Finish the calculation (hint: the z-test statistic will exceed the negative critical cutoff value using a z-table to reject the null hypothesis).

I hope this will help.

Mel · Answer

Thank you very kindly. Helped immensely!