Question

For developing countries in Africa and the Americas, let p₁ and p₂ be the respectiveproportions of babies with a low birth weight (below 2500 grams). A randomsample of n₁ = 2000 African women yielded y₁ = 750 with nutritional anemia anda random sample of n₂ = 2000 women from the Americas yielded y₂ = 650 womenwith nutritional anemia. We shall test H₀: p₁ = p₂ against the alternative hypothesisH₁: p₁ > p₂ at α = 0.05.

1. What is the type of the test?

a) Right-tailed

b) Left-tailed

c) Two-tailed

2. Calculate Observed Test Statistic

3. Find the P-value of the test

4.Find the Critical Value of Critical Region of the Test

5. Draw Your Conclusion of the Test at α = 0.05

a) Fail to Reject H0

b) Reject H0

Answer 1

Solution:

1)

Right tailed test

(because there is > sign in H₁ )

2)

₁ = 750/2000 = 0.375

₂ = 650/2000 = 0.325

= (y1 +y2)/(n1 + n2) = (750+650)/(2000+2000) = 0.35

1 - = 1 - 0.35 = 0.65

The test statistic z is

z =

= (0.375 - 0.325)/[0.35*0.65*((1/2000)+(1/2000))]

= 3.31

Observed Test Statistic z = 3.31

3)

For right tailed test ,

P value = P(Z > z) = P(Z > 3.31) = 0.0005

p value = 0.0005

4)

= 0.05

For right tailed test , critical value is = = 1.645

Critical Value = 1.645

5)

Reject H0

(Because p value is less than )