The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT paper at his university is significantly higher than the national average of 1,300. An accepted standard deviation for LSAT scores is 125. A random sample of 25 scores had an average of 1,375. State the appropriate null and alternative hypotheses.
Calculate the value of the test statistic
Calculate the p-value.
Use the p-value to test the hypotheses and conduct the test at the 0.025 level.

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?