12. Assume the IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Show all work. Just the answer, without supporting work, will receive no credit. (a) If a random sample of 25 adults is selected, what is the standard deviation of the sample mean? What is the probability that 25 randomly selected adults will have a mean IQ score that is between 95 and 105? (b) 13. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 95% confidence interval estimate of the proportion of adults believing in global warming. Show all work. Just the answer, without supporting work, will receive no credit. 14. In a study designed to test the effectiveness of acupuncture for treating migraine, 100 patients were randomly selected and treated with acupuncture. After one-month treatment, the number of migraine attacks for the group had a mean of 2 and standard deviation of 1.5. Construct a 95% confidence interval estimate of the mean number of migraine attacks for people treated with acupuncture. Show all work. Just the answer, without supporting work, will receive no credit. 15. Mimi is interested in testing the claim that more than 75% of the adults believe in global warming. She conducted a survey on a random sample of 100 adults. The survey showed that 80 adults in the sample believe in global warming. Assume Mimi wants to use a 0.05 significance level to test the claim. (a) (b) (c) (d) Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that more than 75% of the adults believe in global warming? Explain. 16. 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) (b) (c) (d) 17. Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion. 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 (a) (b) (c) (d) Brown 42 Yellow 21 Orange 12 Green 7 Tan 18 Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer. 18. 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). x y (a) (b) 19. 0 1 1 2 2 4 5 8 Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. Based on the equation from part (a), what is the predicted value of y if x = 3? Show all work and justify your answer. A farmer is interested in whether there is any variation in the weights of apples between two trees. Data collected from the two trees are as follows: Her null hypothesis and alternative hypothesis are: (a) (b) (c) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to justify the rejection of H0 at the significance level of 0.05? Explain. 20. A study of 5 different weight loss programs involved 250 subjects. Each program was followed by 50 subjects for 12 months. Weight change for each subject was recorded. Mimi wants to test the claim that the mean weight loss is the same for the 5 programs. (a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work): Source of Variation Sum of Squares (SS) Degrees of Freedom (df) Mean Square (MS) Factor (Between) Error (Within) Total (b) (c) 42.36 1100.76 249 Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit