The inside diameter of a randomly selected piston ring is a random variable with mean value 16 cm and standard deviation 0.04 cm.
(a) if x is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of x centered and what is the standard deviation of the x distribution? (enter your standard deviation to five decimal places.) center cm standard deviation cm
(b) answer the questions posed in part (a) for a sample size of n = 64 rings. (enter your standard deviation to five decimal places.) center cm standard deviation cm

Two researchers are attempting to create a new psychotherapy protocol that more reduces panic attacks. they believe that they have succeeded and are now in the clinical trial period of their protocol's development. they are working with several cohort groups, some of which have been through the new protocol, while others have done the standard protocol currently recommended. if these researchers are interested in evaluating the difference in the percentage of test subjects who successfully decreased their panic attacks in 2 months on the new protocol versus the percentage of test subjects who successfully decreased their panic attacks in 2 months with the traditional protocol, which of the following statistical tests would be most appropriate? a. analysis of variance (anova) b. correlation c. chi-square test d. paired t-test e. independent t-test