SOLUTION: Educators claim that 75% of all high school students will attend college next fall. At Beechnut High School, with an enrollment of 818 seniors, a study found 645 will attend colleg

Question 1115335: Educators claim that 75% of all high school students will attend college next fall. At Beechnut High School, with an enrollment of 818 seniors, a study found 645 will attend college in the fall. At = 0.05, test the claim that at least 75% of all high school students will attend college in the fall. Use the P-value method.
A) With a test value of 2.54, the P-value > 0.05. Do not reject the null hypothesis.
B) With a test value of 2.54, the P-value < 0.05. Reject the null hypothesis.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

p = population proportion of high school students that will attend college in the fall

Null Hypothesis:
H0: p >= 0.75

Alternative Hypothesis:
H1: p < 0.75

This is left-tailed test based on the inequality in the alternative hypothesis H1

Since this is a left tailed test, this means we will use the area under the curve to the left of the z-score 2.54

Using a calculator or a table, you'll find that the area under the curve to the left of z = 2.54 is approximately 0.9945

The approximate P-value is 0.9945 which is larger than alpha = 0.05

So because P-value > alpha, this means we fail to reject the null hypothesis. In other words, we do not reject the null hypothesis.

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