Assignment 3 Due Date: April 1, 2011. Material Covered: Lessons 13 through 20. Question 1 Please find the limit(s) of the boundaries for the critical region for the following hypotheses (You only need to find the z, t, or F-critical value in all cases, e.g., +/2.33. Please do not complete the hypothesis test): a. Ho: µd = 5.5, Ha: µd > 5.5, a = 0.15, n = 35, s = 2.5. b. Ho: µ1 – µ2 = 0, Ha: µ1 – µ2 > 0, a = 0.05, n1 = 19, n2 = 25 (s1 = s2). c. Ho: µ1 = µ2 = 0, Ha: µ1 = µ2 < 0, a = 0.1, n1 = 14, n2 = 27 (s1 ? s2). d. Ho: s1 2 = s2 2, Ha: s1 2 ? s2 2, a = 0.05, n1 = 31, n2 = 21 s1 = 8.3, s2 = 4.1. e. Ho: s1 2 = s2 2, Ha: s1 2 ? s2 2, a = 0.01, n1 = 29, n2 = 23 s1 = 7.2, s2 = 10.6. Question 2 A group of ten students from the course INTE 296 was approached by a famous scientist by the name of Dr. Wild E. Coyote with an experimental drug to aid in their retention of statistical procedures. The drug, called Memoraid™, was administered after the students completed a generic, comprehensive exam. Twenty-four hours later, the students were given a similar exam, and the test scores were compared. Based on the following table, is there enough evidence to conclude that the drug was effective in increasing their statistical ability? Use an alpha value of 0.10 and find the p-value. Student 1 2 3 4 5 6 7 8 9 10 Before 75 62 67 70 55 59 60 64 72 65 After 77 65 68 72 62 62 60 67 75 58 Question 3 You have been asked to compare two neighbourhoods in the west end of Montreal by a real estate agency. The agency wants to know if a difference exists in the selling price of houses on Westminster street (Montreal West), as compared to Beaconsfield street (NDG). You take a sample of houses sold on both streets over the past 10 years, adjust the inflation and monetary rate so as to equalize the dollar, and tabulate your results. Is there enough evidence to prove that the selling price for the houses on the two streets is significantly different? Please conduct a complete hypothesis test at the 95% confidence level and calculate the p-value. (Hint: Can we assume that the variances are equal?) Street n ?? s Westminster 16 $125,900 $2400 Beaconsfield 20 $128,800 $3900 Question 4 It has long been suggested that narcotic drugs are more prevalent in “big cities”. In other words, an increase in the size of the community will subsequently entail a rise in the rate of narcotic drug usage. From a random sample of 22 cities of various sizes, a sociologist examines this claim. She collects data from police records regarding violations of the narcotic drug laws per 100,000 inhabitants. The communities were broken down into 4 sizes (large cities, small cities, suburban communities, and rural communities), and data was collected over the period of one calendar year. Using the table found below, please determine if there is significant evidence to conclude that the mean rates of arrests for narcotics is different in each community (based on their size). Please conduct this test at the 99% confidence level. City Community Large Small Suburban Rural 45 23 25 8 34 18 17 16 41 27 19 14 42 21 28 17 37 26 31 10 34 37 Question 5 While coaching your local peewee hockey team, you have always preached to your players that the more shots they get on the opposition’s net, the better the chance your team has of scoring a goal. Some of the parents have questioned this theory, insisting that it would be better if the players waited for favourable scoring opportunities to shoot so that they would not give up the puck so easily. In an effort to quell this argument, you turn to your statistics training and decide to conduct your own investigation based on your team’s performance after their first 10 games of the season. The result of your assessment is found in the table below. Game Shots (y) Goals (x) Game Shots (y) Goals (x) 1 25 2 6 23 2 2 38 5 7 30 3 3 43 7 8 45 5 4 32 5 9 46 4 5 36 4 10 37 3 a. Find the linear equation of regression for the line of best fit. b. Compute the correlation coefficient (r). c. Estimate the number of shots that would be needed in order to score 8 goals. d. If it is known that 43 shots have been taken by your team in a given game, predict how any goals have been scored. e. Conduct a complete hypothesis test using the graphical and p-value method to determine if the population correlation coefficient (r) is equal to 0. Your confidence level should be set at 95%, and your conclusion should refer back to your claim regarding shooting and scoring.