Posted by **Candy** on Wednesday, July 29, 2009 at 5:42pm.

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?

- business statistics -
**MathGuru**, Thursday, July 30, 2009 at 8:48am
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.

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