Instructions: Follow the 6 steps in solving the problems. 1. State the null and alternative hypothesis. 2. Set the alpha level, deg. of freedom and t critical values. 3. Collect the data. 4. Calculate the statistics. 5. Make a decision concering to null hypothesis. 6. Conclusion PROBLEMS: Problem 1 The manager of the packaging process at a cereal manufacturing plant wants to determine if the cereal filling process is in control. The process requires no corrective action if the correct amount of cereal per box is 368 grams. To study this, random samples of 25 boxes were weighed. The sample mean is 372.5 and the process standard deviation is 15. Is there evidence that the weight is different from 368 grams? Use 0.05 as significance level. Problem 2 A group of statistics students recently stated that one of the difficulties they had with learning statistics was the time of day the class was offered. This particular statistics class had always been offered at 3:30 PM, and the students stated that they learned better in the morning. To test this hypothesis, the instructor offered a 10 AM section. The morning class was given the same final examination that had always been used in the class. The instructor knew that the previous classes had an average score of 33 on the final. The 20 students in the AM section earned an average score of 38, with a standard deviation of 2.2. Were these student's scores significantly different than the population? Problem 3 A recent survey indicated that the general population of people rated affirmative action plans in the workforce with a mean of 62. The researcher believes that in a more educated workforce, affirmative action plans would receive a higher rating. She randomly selected a dozen college professors from across the country to complete the survey, and below are her results. Survey: 77 70 68 63 58 64 60 70 63 77 72 61 Did these college professors rate affirmative action plans significantly higher than the general population? Solve this directional problem with an alpha level set to 0.01. Problem 4 In national use, a vocabulary test is known to have a mean score of 68 and a standard deviation of 13. A class of 19 students takes the test and has a mean score of 65. Is the class typical of others who have taken the test? Assume a significance level of 0.05. Problem 5 A sample of 12 machine pins has a mean diameter of 1.15 inches, and the population standard deviation is known to be 0.04. What is a 99 percent confidence interval of diameter width for the population? Problem 6 The data below provide scores from a test taken by ten undergraduate students in statistics this semester. Typically students are given this test at the end of each semester. In the population of students, the mean on this test is equal to 50. Do the ten scores in this sample significantly differ from the population mean? Scores: 63 56 47 48 52 51 58 55 41 47 Problem 7 Intelligence tests are constructed such that the average score among adults is 100 points. Six undergraduate students from Cebu Technological University were given the test and have the following scores: Person 1: 110 , Person 2: 118, Person 3: 110, Person 4: 122, Person 5: 110, Person 6: 150. Can we conclude that these university students were smarter than the average? Problem 8 Suppose you are concerned about the amount of violence on TV and decide to randomly select 10 TV programs, watch them, and count the number of "violent scenes" in each. The data were collected: 32 12 20 10 4 18 25 26 17 14. Is there evidence that the (claim) number of "violent scenes" is at least 21 scenes? Assume an alpha level = 0.05