business statistics
posted by Candy on .
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?

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.