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1. A group of professors investigated first-year college students’ knowledge of astronomy. One concept of interest was the Big Bang Theory of the creation of the universe. In a sample 0f 141 freshman students, 35 believed that the Big Bang Theory accurately described the creation of plantery systems. Baesd on this information, is it correct at the α = 0.01 level of significance to state that more than 20% of all freshman college students believe the Big Bang theory describes the creation of planetary systems? 2. A study was conducted to evaluate the effectiveness of a new mosquito repellent designed by the U.S. Army to be applied as camouflage face paint. The repellent was applied to the forearms of 5 volunteers who then were exposed to 15 active mosquitos for a 10-hour period. The percentage of the forearm surface area protected from bites (called percent repellency) was calculated for each of the five volunteers. For one color of paint (loam), the following summary statistics were obtained: x =83%, s = 14%. Complete parts a and b. 3. A study of n = 110,000 first-time candidates for an exam found that the number of semester hours of college credit taken by the sampled candidate is summarized by x = 146.78 and s = 20.44. A professor claims that the true mean number of semester hours of college credit taken is 146. 4. Suppose 36 0f 104 randomly selected shoppers believe that “Made in the USA” means that 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe “Made in the USA” means 100% of labor and materials are from the United States. Complete parts a through e. 5. The final scores of games of a certain sport were compared against the final point spreads establiished by oddmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 240 games. The sample mean and sample standard deviation of the point-spread errors are x = 1.7 and s = 14.6. Use this information to test the hypothesis that the true mean point-
spread error for all games is lareger than 0. Conduct the test at Îą = 0.05 and interpret the result.