Question

In: Statistics and Probability

For developing countries in Africa and the Americas, let p1 and p2 be the respectiveproportions of...

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

Solutions

Expert Solution

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 )


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