13) According to an article in Newsweek , the natural ratio of girls to boys is

Question

13) 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 64 girls and 86 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.

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

(Part d) State the distribution to use for the test. (Round your standard deviation to four decimal places.)

P' ~ ( , )

(part f). What is the p-value? (Round your answer to four decimal places.)
  
( )
Explain what the p-value means for this problem.

If H0 is true, then there is a chance equal to the p-value that the sample ratio is 64 out of 150 or less OR 76 out of 150 or more.

If H0 is true, then there is a chance equal to the p-value that the sample ratio is not 64 out of 150 or less OR 76 out of 150 or more.     

If H0 is false, then there is a chance equal to the p-value that the sample ratio is not 64 out of 150 or less OR 76 out of 150 or more.

If H0 is false, then there is a chance equal to the p-value that the sample ratio is 64 out of 150 or less OR 76 out of 150 or more.

(part g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

(Part I) 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. (Round your answers to four decimal places.)

Explanation / Answer

Ans:

Sample proportion=64/150=0.4267

standard deviation=sqrt(0.467*(1-0.467)/150)=0.0407

Test statistic:

z=(0.4267-0.467)/sqrt(0.467*(1-0.467)/150)

z=-0.99

p-value(2 tailed)=2*P(z<-0.99)=0.3221

If H0 is true, then there is a chance equal to the p-value that the sample ratio is 64 out of 150 or less OR 76 out of 150 or more.

95% Confidence interval for true proportion

=0.4267+/-1.96*sqrt(0.4267*(1-0.4267)/150)

=0.4267+/-0.0792

=(0.3475, 0.5058)

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