Question

For one binomial experiment,

n₁ = 75

binomial trials produced

r₁ = 45

successes. For a second independent binomial experiment,

n₂ = 100

binomial trials produced

r₂ = 65

successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.

(d) Compute p̂1 - p̂2. p̂1 - p̂2 =

Compute the corresponding sample distribution value. (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.)

(e) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer 1

Given that,

For sample 1 : n1 = 75, x1 = 45 and

For sample 2 : n2 = 100, x2 = 65 and

Pooled proportion is,

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

d) p̂1 - p̂2 = 0.6 - 0.65 = -0.05

=> p̂1 - p̂2 = -0.05

Test statistic is,

=> Test statistic = Z = -0.68

e) p-value = 2 * P(Z < -0.68)

=> p-value = 2 * [ 1 - P(Z < 0.68) ]

=> p-value = 2 * [ 1 - 0.7517 ]

=> p-value = 2 * 0.2483

=> p-value = 0.4966

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