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# One-Tailed and Two-Tail Hypothesis Tests

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1) For a simple random sample , n= 700 and p= 0.63. At the 0.025 level, test H0: &#960; &#8804; 0.60 versus H1: &#960; 0.60 (&#960; this symbol represents Pi)

2) 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 of 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 the directors claim?

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For a simple random sample , n= 700 and p= 0.63. At the 0.025 level, test H0: π ≤ 0.60 versus H1: π > 0.60 (π this symbol represents Pi)
Answer
H0: π ≤ 0.60
H1: π > 0.60
Test Statistic used is
Decision rule: Reject the null hypothesis if the calculated value of Z is greater than the critical value of Z
Details
Z Test of Hypothesis for the Proportion

Data
Null Hypothesis p= 0.6
Level of Significance 0.025
Number ...

#### Solution Summary

This solution conducts a one-tailed and two-tailed hypothesis test by providing a null and alternative hypothesis. It then calculates the test statistic in each scenario to compare to the p-value. A decision is then made to accept or reject the null hypothesis.

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