The table shows whether pre-heating the oven or not pre-heating the oven affected the outcome of a dish (which typically does not require a pre-heated oven):

success failure Total

no pre-heat 22 4 26

pre-heat 10 6 16

Total 32 10 42

1) To find the equality of the success probabilities, try a score test and Pearson chi-square test. What are the results?

2) Calculate the odds ratio and corresponding confidence interval for it.

3) Calculate the relative risk and confidence interval for it. What does this mean?

4) What are the Wald confidence intervals for the difference in probabilities of success conditioning on the instructions? Show the calculations.

5) Is there enough evidence to conclude that pre-heating is a good option? Why?