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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.

Respuesta :

Answer:

The claim is valid

Step-by-step explanation:

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

[tex]H_0: p =0.75\\H_a: p \geq 0.75[/tex]

(Right tailed test at 5% significance level)

Sample size n = 818

Sample favourable x = 645

p = sample proportion = [tex]\frac{645}{818} \\\\=0.7886[/tex]

Assuming H0 to be true std error of p = [tex]\sqrt{\frac{pq}{n} } \\=0.01514[/tex]

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.

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