A magician began to do a trial of the YSORT method designed to increase the probability of drawing a 1 out of a two card deck with numbers 1 and 2.

291 attempts were made using the YSORT method and 239 of the draws were 1's. How can you use a significance level to test this claim that the YSORT method is effective in increasing the chances that a drawn card will be a 1?

1. What would be the null and alternate hypotheses written mathematically? what claim supports this?
2. What is the test statistic?
3. What is the Rejection region (critical region) and fail to reject region? what would it be like through a drawing curve that separates the rejection region from the fail to reject region using the critical value?
4. What is the p-value? what is the p-value's meaning?
5. How can we decide whether to reject or fail to reject the null using the p-value approach?
6. What is an interpretation of the decision in the context of the claims?
7. What is a Type-1 error in this problem? What are the issues of the problem?
8. Using sample data, how can a 98% confidence interval estimate of the proportion of 1's be calculated? What does the confidence interval say about the claim that the magician's YSORT method works in giving better chances that a drawn card will be a 1?