Eighteen technicians in a cell phone repair shop are randomly selected to participate in a study comparing two screen repair techniques. They are randomly assigned one of the two techniques. The manager trains 9 technicians on one technique and trains the other 9 technicians on the second technique. He then records the number of screen repairs each technician does in one week. Which inferential statistical test would be most appropriate for this scenario?

a. A one-sample z-test
b. A paired t-test
c. A chi-square goodness-of-fit test
d. A one-sample t-test
e. A two-sample t-test

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.