Question

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p=0.58 versus H1: p<0.58 n=150, x=78, α=0.05

1. Is np0 (1 minus p 0) ≥10? Yes or No?

2. Use technology to find the P-value. P-value=

(Round to three decimal places as needed.)

Answer 1

1) 1) np₀(1 - p₀) = 150 * 0.58 * (1 - 0.58) = 36.54

Yes, np₀(1 - p₀) > 10

2) = x/n = 78/150 = 0.52

The test statistic z = ( - p)/sqrt(p(1 - p)/n)

                             = (0.52 - 0.58)/sqrt(0.58 * (1 - 0.58)/150)

                             = -1.49

P-value = P(Z < -1.49)

              = 0.068