Q: The Genetics and IVF institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. Assuming 291 babies have been born and using the YSORT method with 239 being boys how can we use a significance level of 0.05 to test the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy?

1. What is the null and alternate hypotheses written mathematically? what is the claim?
2. What is the test statistic?
3. How can we identify the rejection region (critical region) and fail to reject region? How do we show this by drawing a curve separating the rejection region from the fail to reject region using the critical value?
4. What is the p-value and what does it mean?
5. Should we reject or fail to reject the null using the p-value approach?
6. What would our interpretation of the decision in the context of our claim?
7. What is the type 1 error in this problem? what is its consequences in the context of the problem?
8. Using the sample data to construct a 90% confidence interval, what would we estimate the proportion of boys? What does the confidence interval suggest about the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy? (P>0.5) (show using technology)