Consider the hypothesis test below.

h 0: p 1 - p 2 0
h a: p 1 - p 2 > 0

the following results are for independent samples taken from the two populations.

sample 1 sample 2
n1 = 200 n2 = 300
p1 = 0.28 p2 = 0.15
what is the value of the test statistic (to 2 decimals)?

what is the p-value (to 4 decimals)?

with = .05, what is your hypothesis testing conclusion?

p-value: 0.0367

Decision: Reject H₀

Step-by-step explanation:

Hello!

Hypothesis to test:

H₀:ρ₁-ρ₂=0

H₁:ρ₁-ρ₂>0

The statistic to use to test the difference between two population proportions is the approximation of Z

Z=     (^ρ₁-^ρ₂)-(ρ₁-ρ₂)       ≈N(0;1)

   √ (^ρ₁(1-^ρ₁))/n₁)+(^ρ₂(1-^ρ₂)/n₂))

Z=                    (0.28-0.15)-0                    = 1.79

   √ (0.28(1-0.28)/200)+(0.15(1-0.15)/300)

p-value

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

P(Z>1.79)= 0.0367

Conclusion:

Comparing the p-value against the significance level, you can decide to reject the null hypothesis.

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