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Xan article in the washington post on march 16, 1993 stated that nearly 45 percent of all americans have brown eyes. a random sample of n=80 c of i students found 30 with brown eyes. we test h0:p=.45 ha:p?.

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jepessoa

Answer:

(a) What is the z-statistic for this test?

  • z = -1.35

(b) What is the P-value of the test?

  • P-value = 0.0885

Explanation:

n = 80

x = 30

H₀:p = 0.45

Hₐ:p ≠ 0.45

Now to find z statistic we will use one sample proportion test

[tex]\widehat{p}\\[/tex] = X / n = 30 / 80 = 0.375

z = ([tex]\widehat{p}\\[/tex] - p) / √{[p(1 - p)] / n}

z = (0.375 - 0.45) / √{[0.45(1 - 0.45)] / 80} = -1.3484 or -1.35

P-value for z value for -1.35 (using table) = 0.0885

z = -1.35 and P-value = 0.0885

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