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 61 girls and 89 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.
i. state the null and alternative hypothesis

ii.In words, state what your random variable P' represents.

iii. State the distribution to use for the test. (Round your answers to four decimal places.)
P' ~ ??? (???,???)

iv. What is the test statistic?

v. What is the p-value? (Round your answer to four decimal places.) and what does it mean?

vi. Sketch a picture of this situation.

vii. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

viii. Construct a 95% confidence interval for the true proportion.

Answer 1

Answer:

Given,

Ho : p = 0.467

Ha : p != 0.467

sample proportion p^ = x/n = 61/150 = 0.407

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

substitute values

= (0.407 - 0.467)/sqrt(0.467(1-0.467)/150)

z = - 1.47

P value = 0.1415618 [since from z table]

= 0.1416

Here we observe that, p value > alpha, so we fail to reject Ho.

Here at 95% CI, z value is 1.96

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

substitute values

= 0.407 +/- 1.96*sqrt(0.407(1-0.407)/150)

= 0.407 +/- 0.0786

= (0.3284 , 0.4856)