Question

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.

Answer 1

The claim is valid

Explanation:

Given that educators claim that 75% of all high school students will attend college next fall.

`H_0: p =0.75\\H_a: p \geq 0.75`

(Right tailed test at 5% significance level)

Sample size n = 818

Sample favourable x = 645

p = sample proportion =
`(645)/(818) \\\\=0.7886`

Assuming H0 to be true std error of p =
`\sqrt{(pq)/(n) } \\=0.01514`

Test statistic Z = p difference/std error

= 2.55

Z critical for 95%one tailed is 1.645

Since test statistic >1.645 we reject H0

The claim is valid.