Question

9. Congenital heart disease affects 1 out of every 120 live born infants in the United States. A Minnesota researcher is going to randomly sample 2,000 birth records in one Minnesota county and compare the county rate to the national rate. Let X represent the number of infants diagnosed with congenital heart disease in the sample from the Minnesota county. (d) The sample from the Minnesota county shows that there were 25 infants diagnosed with congenital heart disease. Given the national rate, do you consider the observation of 25 infants affected out of 2,000 births to be statistically unusually high? State why or why not.

Answer 1

Population Proportion = 1/120 = 0.008

Sample

n = 2000

Proportion = 25/2000 = 0.013

Alpha = 0.05

Null and Alternate Hypothesis

H₀: p = 0.008

H_a: p > 0.008

Test Statistic

z = (p – p₀)/{p₀*(1-p₀)/n}^1/2 = (0.013 – 0.008)/{0.008*(1-0.008)/2000}^1/2

= 2.05

P-value = P(z>2.05) = 1- P(z<2.05) = 1 - 0.9798 = 0.0202

Result

Since the p-value is greater than 0.05, the data is not statistically significant and we fail to reject the null hypothesis.

Conclusion

Hence, we do not consider the observation to be statistically unusually high