1) The figure below shows a randomization distribution for testing Ho : / = 50 vs Ha : A 0.45 for a population proportion along with the sample data p = 63 125 = 0.504. Use StatKey or other technology to generate a randomization distribution and calculate the p-value. p-value: 3) Sleep or Caffeine for Memory? Caffeine is often used by adults to replace the need for sleep and to benefit alertness. One study compares students' ability to recall memorized information after either the consumption of caffeine or a brief sleep. A random sample of 24 adults (between the ages of 18 and 39) were randomly divided into two groups of 12 and verbally given a list of 24 words to memorize. During a break, one of the groups takes a nap for an hour and a half and the other group is kept awake and then given a caffeine pill an hour prior to testing. The response variable of interest is the number of words participants are able to recall following the break. For the sleep group, 71 = 15.25 with n = 12, and for the caffeine group, 12 = 12.25 with n = 12. We are interested in testing whether there is evidence of a difference in average recall ability between the two treatments. (a) Define the relevant parameters and state the null and alternative hypothesis. (b) Using StatKey, create a randomization distribution (go to Randomization Test for a Dif- ference in Means in StatKey and select the SleepCaffeineWords dataset) using n = 5000 samples and compute the p-value. (c) Using a 1% significance level, state the the formal conclusion of test and the conclusion of the test in context