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 59 girls and 91 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7? Conduct a hypothesis test at the 5% level.

Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

Answer 1

Answer:

Given,

Ho : p = 0.467

Ha : p != 0.467

alpha = 0.05

x = 59

sample n = 150

sample proportion p^ = x/n = 59/150 = 0.3933

test statistic z = (p^ - p)/sqrt(p(1-p)/n)

substitute values

= (0.3933 - 0.467)/sqrt(0.467(1-0.467)/150)

= -1.81

P value = 2*P(z < - 1.81)

= 0.0702958 [since from z table]

= 0.0703

Here p value > 0.05, so we fail to reject Ho.

95% CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.3933 +/- 1.96*sqrt(0.3933(1-0.3933)/150)

= 0.3933 +/- 0.0399

= (0.3534 , 0.4332)

95% CI is 0.3534 < p < 0.4332