P age |1 Assignment # 5. Due on Tuesday August 09, 2016 at 4 pm Date of Submission: Course Number: 03-65-205-91 Course Title: Statistics for the Sciences (Distance Education) Instructor: Dr. Kazi Azad Submitted By: Last Name: First Name: ID #: Address: Do Not Write Anything Below This Line Question # 1 2 3 4 5 6 7 8 9 10 Total Actual Mark 10 8 12 8 10 8 12 10 14 8 100 Obtained Mark P age |2 Instructions to complete the assignment: 1. Do all the problems and do by yourself 2. Print Page 1. Fill in it with your information and use it as the cover page for the assignment (must attach this with the assignment). For your convenience, I upload the cover page as a separate Word document also. Without the cover page your assignment will not be graded! 3. Assignments can be submitted as hand written or typed in the computer 4. Please write assignments legibly and keep at least a 1 inch margin on the left edge 5. Write your complete address on the cover page as well as on the envelope 6. Make sure you staple the assignment pages with the cover page. Write your last name on top of each page with page number. I will not be responsible for any missing page Note: Keep a copy of your submitted assignment! Instructions for online submission of the assignment are posted on blackboard on \"Assignments\" link page. No email attachment please! If there is no postal strike, you can send the assignment by post and must be postmarked no later than 4:00 PM on the deadline date. Post assignments to: Dr. Kazi Azad RE: 65-205-91 Distance Education Department of Mathematics and Statistics University of Windsor 401 Sunset Ave Windsor, Ontario, N9B 3P4, Canada If you wish to personally drop off your assignment at the department, please drop it off at: Lambton Tower, Room 10-109 (Dina Labelle). You should submit your assignment by 4:00 pm on the due date. P age |3 Problems. 1. (10 marks) The test scores on a 100-point test were recorded for 20 students: 71 73 84 77 93 86 89 68 91 82 67 65 86 76 62 75 75 57 72 84 a. Can you reasonably assume that these test scores have been selected from a normal population? Use a stem and leaf plot to justify your answer. b. Do the sample data suggest that the average test score is more than 75? Use = 0.05. c. If these students can be considered a random sample from the population of all students, find a 95% confidence interval for the average test score in the population. 2. (8 marks) A cannery prints \"weight 454 grams\" on its label. The quality control supervisor selects nine cans at random and weighs them. He finds = 445 and = 14.2. Do the data present sufficient evidence to indicate that the mean weight is less than that claimed on the label? Test using = 0.05 by applying both p-value approach and critical value approach. 3. (12 marks) The numbers of raisins in each of 14 miniboxes (15g) were counted for a generic brand and for Sunmaid brand raisins: Generic Brand 25 26 25 26 28 28 26 27 24 26 26 28 27 25 25 28 25 28 Sunmaid 29 24 24 28 28 30 24 24 22 27 a. Are you willing to assume that the underlying population variances are equal? Why? b. Use the critical value approach and p-value approach to determine whether there is a significant difference in the mean numbers of raisins per minibox. Use = 0.05. What are the implications of your conclusion? c. Determine a 95% confidence interval estimate for (1 2). Does your interval estimate substantiate your conclusion in part a? Explain. 4. (8 marks) An article in Archaeometry involved an analysis of 48 samples of Romano-British pottery, found at four different kiln sites in the United Kingdom. The samples were analyzed to determine their chemical-composition. The percentage of aluminum oxide found in the samples of two sites is shown below. Island Thorns Ashley Rails 18.3 17.7 15.8 18.3 18.0 16.7 18.0 14.8 20.8 19.1 P age |4 a. Do the data provide sufficient information to indicate that there is a difference in the average percentage of aluminum oxide at the two sites? Test at the 5% level of significance. b. Find the approximate p-value for the test. 5. (10 marks) An advertisement for Food Basics claims that Food Basics has had consistently lower prices than four other full-service supermarkets. As part of a survey conducted by an \"independent market basket price-checking company,\" the average weekly total, based on the prices (in $) of approximately 95 items, is given for two different supermarket chains recorded during 4 consecutive weeks in a particular month. Week 1 2 3 4 Food Basics 254.26 240.62 231.90 234.13 Zehrs 256.03 255.65 255.12 261.18 a. Is there a significant difference in the average prices for these two different supermarket chains? b. What is the approximate p-value for the test conducted in part a? c. Construct a 99% confidence interval for the difference in the average prices for the two supermarket chains. Interpret this interval. 6. (8 marks) To test the comparative brightness of two red dyes, nine samples of cloth were taken from a production line and each sample was divided into two pieces. One of the two pieces in each sample was randomly chosen and red dye 1 applied; red dye 2 was applied to the remaining piece. The following data represent a \"brightness score\" for each piece. Sample Dye 1 Dye 2 1 10 8 2 12 11 3 9 10 4 8 6 5 15 12 6 12 13 7 9 9 8 10 8 9 15 13 a. Is there sufficient evidence to indicate a difference in mean brightness scores for the two dyes? Use = 0.05. b. Find the approximate p-value for the test and interpret its value. 7. (12 marks) The fasting blood glucose level of a randomly selected person was measured for seven days and the following readings were made: 7.0, 7.7, 6.8, 7.1, 7.1, 6.1, 7.3. It is reasonable to assume that the glucose level distribution is normal. A diabetes researcher would like to study the variability in the fasting blood glucose level readings for the selected person. The researcher believes that fasting blood glucose never varies more than 0.8 mmol/L. It is of interest to determine if the sample data present sufficient evidence to reject the researcher's claim. a. b. c. d. State the appropriate null and alternative hypotheses. What is the appropriate conclusion at the 0.05 level of significance? What is the approximate p-value for the test statistic? Estimate the population variance using a 90% confidence interval. P age |5 e. Can we infer at the 90% confidence that the population variance is significantly less than 1? 8. (10 marks) Independent random samples from two normal populations produced the given variances: Sample Size Sample Variance 13 18.3 13 7.9 a. Do the data provide sufficient evidence to indicate that 12 > 22 ? Test using = 0.05. b. Find the approximate p-value for the test and interpret its value. c. Construct a 95% confidence interval for the variance ratio. Interpret the interval. 9. (14 marks) The SAT subject tests in chemistry and physics for two groups of 15 students each electing to take these tests are given below. Chemistry Physics = 644 = 658 s = 114 s = 103 n = 15 n = 15 a. To use the two-sample t test with a pooled estimate of 2, you must assume that the two population variances are equal. Test this assumption using the F test for equality of variances. What is the approximate p-value for the test? b. Construct a 90% confidence interval for the variance ratio. c. Now use the two-sample t test to detect a difference between the two population means. State the null and alternative hypotheses for the test. Test using = 0.01 and state your conclusions. d. Find the approximate p-value for the test. e. Find a 99% confidence interval for (1 2 ). Interpret the interval. 10. (8 marks) The calcium (Ca) content of a powdered mineral substance was analyzed 10 times with the following percent compositions recorded: 0.0271 0.0271 0.0282 0.0281 0.0279 0.0269 0.0281 0.0275 0.0268 0.0276 a. Find a 99% confidence interval for the true calcium content of this substance. b. What does the phrase \"99% confident\" mean? c. What assumptions must you make about the sampling procedure so that this confidence interval will be valid? What does this mean to the chemist who is performing the analysis