Mathematics 1670 Statistics Assignment #2 (Value: 10%) Due: June 9th@12 noon Directions: Answer all questions, show all workings. Submit your completed work via one of the approved methods (pdf preferred) through the MA1670 Assignment #2 electronic dropbox in D2L. Each student is responsible for solving/writing up and submitting their own individual work. Sampling 1. Listed below are 20 Insurance agents in the St. John's-Mount Pearl area: Id # 1 2 3 4 5 Name Pearl Cal Ed Fred Wanda Id # 6 7 8 9 10 Name Mary Beth Francis Ralph Zike Id # 11 12 13 14 15 Name Denise Walter Sam Mac John Id # 16 17 18 19 20 Name Jim Robert John #2 Barry Todd a) We want to randomly select four dealers, so we place each id number in a hat and pick out four numbers. The id numbers are: 2, 10, 11, & 19. Name the agents that would be included in this sample? What kind of sampling is this? b) Use a table of random numbers to select your own sample of four agents (Appendix B.5 in text). What kind of sampling is this? Note: You must explain step by step what you did? c) A sample of four dealers is to consist of every fifth agent. The number 2 is selected as the starting point. Name the agents that will be included in this sample? What kind of sampling is this? Central Limit Theorem 2. The weights of all NHL goalies are not normally distributed with a mean of 183.5 pounds & standard deviation of 8.8 pounds. A sample of 36 goalies are weighed, calculate the probability that the sample's mean weight is between 185.0 and 186.0 pounds? 3. A company that makes light bulbs claims that its bulbs have an average life of 750 hours with a standard deviation of 18 hours. A random sample of 60 light bulbs is taken. Let be the mean life of this sample. a) What is the probability that > 755 hours? b) What is the probability that 740 hours < < 755 hours? (ie. Find the probability of the mean life being between 740 & 755 hours) Note: On the hypothesis testing questions you must use the five-step process. Hypothesis Testing (One Sample -- mean) 4. The Thompson's Discount Store chain issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance is more than $400. A random check of 172 unpaid balances revealed the sample mean to be $407 and the standard deviation of the population is $38. Using hypothesis testing can the credit manager conclude the population mean is greater than $400 at the 0.05 significance level? 5. A physician claims that joggers' maximal volume oxygen intake is greater than the average of all adults. A sample of 19 joggers has a mean of 43.6 milli-litres per kilogram (ml/kg) and a standard deviation of 6 ml/kg. If the average of all adults is 40.7 ml/kg, using hypothesis testing is there enough evidence to support the physician's claim at a level of significance of 0.01. Assume that jogger's maximal volume oxygen intake is normally distributed. Hypothesis Testing (One Sample - proportion) 6. Use hypothesis testing to test the claim that the percentage of women earning a bachelor's degree in business is less than 50%. A random sample of 200 business graduates earning a bachelor's degree in business found that 85 of them were women. Use a level of significance of 0.01 Hypothesis Testing (Two samples - means) 7. The Quick Food Company wishes to compare the weight gain of infants using their brand versus their competitors. A sample of 40 babies using the competitor's products revealed a mean weight gain of 7.6 pounds, in the first two months, with a standard deviation of 2.3 pounds. A sample of 55 babies using the Quick's brand revealed a mean increase in weight of 8.1 pounds, in the first two months, with a standard deviation of 2.9 pounds. At the 0.01 significance level, can we conclude that babies using the Quick's brand gained more weight? Hypothesis Testing (Two samples - proportions) 8. A study by a specific department showed that a person's ability to identify food by smell and taste decreases with increasing age. As a result, the department recommends adding simulated odors to the food of older people to improve its flavor. Part of the department's experiment involved asking a random sample of older persons and a random sample of college students to smell, taste, and identify a variety of foods that had been blended to prevent identification by "feel". Subjects were blindfolded during the experiment. Suppose that blended apple was correctly identified by 81 of 100 students and by 55 of 105 older people. Would these data support the conclusion that the ability to identify food decreases with age? Test using a level of significance of 0.05. Two Sample Hypothesis Test (Dependent Samples) 9. A winery wonders if there is a difference in people's preference between its carbonated wine and its non-carbonated wine. Seven people are given the winery's wine with carbonation then given the same wine without carbonation. After the tasting, each person is asked to give a ranking from 1 to 10 where 1 is \"totally dislike\" & 10 is \"can't live without\". The results are given as follows: Person's Name Rick Hilary Suzanne Denise Velma Paul Doug Ranking with Carbonation 5 8 2 9 6 1 5 Ranking without Carbonation 7 5 3 7 9 8 5 At a level of significance of 0.10, is there a difference in people's preference between its carbonated wine and its non-carbonated wine. We can assume the population of differences follow the normal distribution. Linear Regression: 10. Does your IQ Score determine your Statistics grade? Five randomly selected Statistics students are selected and the person's IQ (x) and the person's grade (y) are recorded below. x(IQ score) 110 90 105 y (grade) 50 44 71 (i) Draw a scatter diagram for the above data 110 61 85 48 (ii) Find the simple linear regression equation that best fits your data using the techniques of linear regression. (iii) If a student has an IQ Score of 130, using your equation from above, what would you predict to be the students grade. (iv) Calculate the linear correlation coefficient (r) of this simple linear regression and interpret its meaning. (ie. Is this linear regression equation good at predicting a student's grade based on IQ score?)