A university professor wanted to know if the attitudes towards stats changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward stats. When the sememster was finished she administered another test to the same group of students and wanted to see if there was a difference b/w the average attitudes towards stats. What type of analysis would be most appropriate analysis? a. matched pairs t test
b. independent t tests
c. one sample t tests
d. none are appropriate

the answer is  

a.

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step-by-step explanation:

it is only things thain can be deafeated

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.