The following sample data have been collected from a paired sample from two populations. the claim is that the first population mean will be at least as large as the mean of the second population. this claim will be assumed to be true unless the data strongly suggest otherwise. sample 1 - 4.4 , 2.7, 1.0, 3.5 , 2.8 sample 2- 3.7 , 3.5, 4.0, 4.9 , 3.1 sample 1- 2.6 , 2.4, 2.0, 2.8 sample 2- 4.2, 5.2, 4.4 , 4.3 a. assume the appropriate null and alternative hypothesis. b. based on the sample data, what should you conclude about the null hypothesis? test using ? =0.10

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?