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 twotail 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 twotailed test because the alternative hypothesis doesn't specify a specific direction)
Using a formula for a binomial proportion onesample ztest 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 ztest statistic will exceed the negative critical cutoff value using a ztable to reject the null hypothesis).
I hope this will help.
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