1. Suppose researchers carry out a one-way ANOVA involving 3 groups. After finding statistically significant evidence of a difference in the group means, they decide to use the Bonferroni correction to come up with simultaneous confidence intervals for the pairwise differences, keeping the family-wise confidence level at least 90%.

Help the researchers out here. Using the Bonferroni approach, what should the confidence level be for the individual intervals?

Important: Enter your answer as a percentage confidence level, but without the percent sign. For example, if your answer is 98.627%, enter 98.627.

(Give your response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols.)

2. Suppose we are interested in calculating a 95% confidence interval for the mean of a normally distributed population. We've drawn a sample of 8 observations from this population, and found a sample mean of 347.4 and a sample standard deviation of 58.0.

What is the appropriate lower endpoint of the 95% interval for mu? (e.g. If the interval is (3.712,9.674), give 3.712 as your response.)

(Give your response to at least 3 decimal places. Give only your numeric response, and no extra characters or symbols.)

3. A person is playing a gambling game with a friend. In this game, there are two urns. Urn 1 contains 9 green balls and 8 red balls. Urn 2 contains 7 green balls and 4 red balls. The game starts with the person tossing a biased coin that comes up heads with probability 0.23 and tails with probability 1-0.23. If the coin comes up heads, the person draws two balls randomly and without replacement from urn 1. Otherwise, they draw two balls randomly and without replacement from urn 2.

The person has flips the coin and draws two balls. What is the probability that both balls are red?

(Give your response to at least 3 decimal places. Give only the numeric response, and not any extra characters or symbols.)