1) In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table. Number of Words Recalled Subject 1 hour later 24 hours later 1 14 12 2 18 15 3 11 9 4 13 12 5 12 12 Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Assume we want to use a 0.10 significance level to test the claim. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work ,steps and formulas (c) Determine the P-value for this test. Show all work, steps and formulas 2) . In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats per minutes. Use a 0.05 significance level to test the researcher's claim.. (a) Identify the null hypothesis and alternative hypothesis. (b) Determine the test statistic. Show all work, steps formulas (c) Determine the P-value for this test. Show all work 3) The UMUC Daily News reported that the color distribution for plain M&M's was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M's was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer. Color Number Brown 42 Yellow 21 Orange 12 Green Tan 11 14 (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work, steps formulas (c) Determine the P-value. Show all work (d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer. 4. A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x0125 y1248 (a) Find an equation of the least squares regression line. Show all work