Question 1 to 5
Year 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Return -5.03 49.88 38.73 -14.19 30.4 -19.86 4.37 -19.41 93.36 -5.42 -4.48 -0.75 -38.92 -3.91 28.82 -7.34 18.33 33.35 59.45 8.09 43.79 34.3 36.13 -56.02 76.46 Brand A Brand B 16 16 14 20 17 18 19 15 19 19 20 21 12 21 16 18 19 20 14 19 15 15 13 13 13 16 15 15 15 19 12 17 15 18 16 16 17 16 16 20 16 12 16 19 19 16 16 15 16 20 16 18 21 14 18 17 21 18 15 17 20 18 13 16 18 18 18 14 21 15 16 20 16 23 18 15 16 16 18 17 \f\fQUESTION 1 1) The weight of competition pumpkins at the Circleville Pumpkin Show in Circleville, Ohio, can be represented by a normal distribution with a mean of 703 pounds and a standard deviation of 347 pounds. a. Find the probability that a randomly selected pumpkin weighs at least 1,622 pounds. (2 Marks) b. Find the probability that a randomly selected pumpkin weighs between 465.1 and 1,622 pounds. (4 Marks) 2) Customers arrive at a drive-through teller window of a bank. They stay in line when the teller is busy. The service time is exponentially distributed with a mean of four minutes. a. What is the probability that the next customer in line will take longer than seven minutes to be served? (2 Marks) b. What is the probability that the next customer in line will take less than eight minutes to be served? (2 Marks) c. What is the probability that the next customer in line will take between three and six minutes to be served? (4 Marks) TOTAL: 14 MARKS QUESTION 2 1) A Family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them than the last 26 houses that sol in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days. a. What assumption regarding the population is necessary for making an interval estimate for the population mean? (2 Marks) b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (4 Marks) 2) A random sample of eight drugstores shows the following prices (in $ of a popular pain reliever:QUESTION 2 1) A Family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them than the last 26 houses that sol in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days. a. What assumption regarding the population is necessary for making an interval estimate for the population mean? (2 Marks) b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (4 Marks) 2) A random sample of eight drugstores shows the following prices (in $ of a popular pain reliever: 3.50 4.00 2.00 3.00 2.50 3.50 2.50 3.00 a. What is the standard deviation for the sample? (2 Marks) b. Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean. (4 Marks) TOTAL: 12 MARKSQUESTION 3 File: Metals. Using data from the past 25 years, an investor wants to test whether the average return of Vanguard's Precious Metals and Mining Fund is greater than 12%. Assume returns are normally distributed with a population standard deviation of 30%. a. State the null and the alternative hypotheses for the test. (2 Marks) b. Calculate the value of the test statistic and the p-value (4 Marks) C. At o = 0.05, what is the conclusion? Is the return of Vanguard's Precious Metal and Mining Fund greater than 12%? (1 Mark) TOTAL: 7 MARKS QUESTION 4 File: Refrigerator longevity. A consumer advocate researches the length of life between two brands of refrigerators. Brand A and Brand B. He collects data (measured in years) on the longevity of 40 refrigerators for Brand A and repeat the sampling for Brand B. a. Specify the competing hypothesis to test whether the average length of life differs between the two brands. (2 Marks) b. Calculate the value of the test statistics and the p-value. Assume that of = 4.4 and of = 5.2 (4 Marks) C. At 5 % significance level, what is the conclusion? (1 Marks) TOTAL: 7 MARKS QUESTION 5 A social scientist wants to determine whether the life expectancy of the Malaysian men is independent of their religious affiliation. A sample of 100 Malaysian men aged 90 years and above is surveyed, and the results are tabulated as shown below: Life expectancy Religion A Religion B Religion C No Religion > 90 years old 27 26 18 29 Test to see whether there is sufficient evidence to indicate that the longevity of men is independent on religious affiliation. Take a= 0.05.QUESTION 4 File: Refrigerator longevity. A consumer advocate researches the length of life between two brands of refrigerators. Brand A and Brand B. He collects data (measured in years) on the longevity of 40 refrigerators for Brand A and repeat the sampling for Brand B. a. Specify the competing hypothesis to test whether the average length of life differs between the two brands. (2 Marks) b. Calculate the value of the test statistics and the p-value. Assume that of = 4.4 and of = 5.2 (4 Marks) c. At 5 % significance level, what is the conclusion? (1 Marks) TOTAL: 7 MARKS QUESTION 5 A social scientist wants to determine whether the life expectancy of the Malaysian men is independent of their religious affiliation. A sample of 100 Malaysian men aged 90 years and above is surveyed, and the results are tabulated as shown below: Life expectancy Religion A Religion B Religion C No Religion > 90 years old 27 26 18 29 Test to see whether there is sufficient evidence to indicate that the longevity of men is independent on religious affiliation. Take a= 0.05. Ho : PA = PB = PC = PNO RELIGION = .25 H1 : PA # PB # Pc # PNO RELIGION # .25 a. What is the critical value of the chi-square? (2 Marks) b. What is the degree of freedom? (2 Marks) c. What is the value of the test statistics of the chi-square? (2 Marks) d. What is the p-value? (2 Marks) e. Can we conclude that the life expectancy of the Malaysian men depends on their religious affiliation? State your reason. (2 Marks) TOTAL: 10 MARKS\f\f
