Question

Advances in medical care such as prenatal ultrasound examination now make it possible to determine a child's sex early in a pregnancy. There is a fear that in some cultures some parents may use this technology to select the sex of their children. A study from Punjab, India, reports that, in 1993, in one hospital, 56.9% of the 640 live births that year were boys. It's a medical fact that male babies are slightly more common that female babies. The study's authors report a baseline for this region of 51.7% male live births. Is there evidence that the proportion of the male births has changed? Assume that significance level of 0.01. Use 8 step procedures to answer this question.

Base on your conclusion of this question, are you at risk of type I or type II error. The answer is to be written in a complete sentence.

Answer 1

Step 1:

Null Hypothesis: The proportion of the male births has not changed

i.e. H0: P = 0.517

Step 2:

Alternative Hypothesis: The proportion of the male births has changed

i.e. H1: P not =  0.517

Step 3: Let the los be alpha = 0.01

Critical z: ±2.5758

Reject H0 if Test statistic Z value is not in the interval (-2.5758, 2.5758)

It is two tailed test

Step 4: Test statistic:

Step 5: Since Z value is not in the Z critical  values so we reject H0

Step 6: P-value = 0.0085

Step 7: Since P-value < alpha 0.01 so we reject H0

Step 8: Thus There is  sufficeint evidence that the proportion of the male births has changed