Question

Consider the following hypotheses:

H0: p = 0.69

H1: p ≠ 0.69
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Given that p = 0.606, n = 160, and a = 0.05, answer the following questions:

a. What conclusion should be drawn?

b. Determine the p-value for this test.

Answer 1

TOPIC:Test for the population proportion.

Define, p= Population proportion. " To { test, Ho : p=0.69 Hi : p *0.69 (=po, say) L . Given a t that, n = sample size = 160. here, ny 30, so we can use the Normal approximation. = 0.606. 6 = sample proportion and a= 0.05. The test - statistic (2). þ-. pe (the) /n 0.606 - 0.69 Jo. 69 x0.31/160 = [-2.297 are = I 26 6 critical values [ Z2 = upper /2-t17 point of N(OD = Z 0.025 = ± 1.96/ From L Normal table]

since lobsenved 21 a lcritical valuce sol, we reject to at x = 0.05 =) Conclusion: Reject to sufficient evidence population proportion at to is a=0.05. There is support that the different from 0.69. [Ano observed (2) = -2.297 2 x 2.297 ZM ® P-value = 2% [2 > 1-2.2971). [z o = 20 (2 * 2.29) [26) = adf of] = 2. {1 - 8 (2-297)} N(O) 892 Comas 72. {-0.9892) Froom Normal table. J. = [0, 0216 / cang