Assume that shoes are produced in three countries: 20 percent in Korea, 40 percent in Canada, and 40 percent in China. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores.   Plant Racing Training Korea 0.45 0.55 Canada 0.65 0.35 China 0.25 0.75 If you purchase a pair of training shoes selected at random, what is the probability that they were made in Korea?

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Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…

You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a)  Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.

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The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Business Humanities. Natural Science Social Science All other subjects USE SALT Percent of Books on Subject in Circulation Library on This Subject 32% 25% 20% 15% 8% Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance? State the null and alternate hypotheses. Ho: The distributions are different. H₁: The distributions are different. H: The distributions are different. H: The distributions are the same. H₁: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are different.…