Question

According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?

Answer 1

Based on the study results, the percentage of girls born in China could range from 32.98% to 47.02%.

Step-by-step explanation:

To determine if the percentage of girls born in China is 46.7%, we can calculate the confidence interval for the proportion of girls in the population using a binomial distribution. Based on the study, out of 150 births, 60 were girls and 90 were boys.

1. Calculate the sample proportion of girls: p = 60/150 = 0.4
2. Calculate the standard error: SE = sqrt((p*(1-p))/n) = sqrt((0.4*(1-0.4))/150) ≈ 0.0357
3. Calculate the margin of error: ME = z*(SE) = 1.96*(0.0357) ≈ 0.0702
4. Calculate the confidence interval: CI = p ± ME = 0.4 ± 0.0702 = (0.3298, 0.4702)

The confidence interval suggests that the true proportion of girls born in China could range from 32.98% to 47.02%. Since the reported figure of 46.7% falls within this interval, it is plausible based on the study results.