Introduction to Statistics assignment2

Introduction to Statistics assignment2 - Assignment 2 Due...

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Unformatted text preview: Assignment 2 Due Date: March 4, 2011. Material Covered: Lessons 9 through 13. Question 1 According to one study, it has been claimed that 65% of all single men in Montreal would welcome a woman taking the initiative in asking for a date. You decide to challenge this study by performing a little experiment of your own. You randomly select 15 single men from around Montreal and ask them if they would be comfortable with a woman asking them out for a date. If the claim made by the study was true, what is the probability that: a) b) c) d) Exactly 9 men would say yes? Exactly 6 men would say no? More than 11 men would say yes? At most 4 men would say no? Question 2 Over the course of a year, the manager of Motel St‐Jacques, located in Brossard, Quebec, has noticed that on average, 170 rooms will be rented out every night, with a standard deviation of 10 rooms. If it is assumed that the probability distribution for the number of room rentals forms a normal distribution, what is the probability that on a given night: a) b) c) d) Less than 155 rooms are rented. More than 190 rooms are rented. More than 164 rooms are rented. Between 162 and 188 rooms are rented. Question 3 You have been studying the effects of different fertilizers on the growth of certain produce. In the latest instalment of your experiment, you are testing Quebec’s own “Gro‐Haut” fertilizer and its effects on carrots. From the sample of carrots that you have measured, you calculate an average length of 24 cm with a standard deviation of 4. Please construct a confidence interval for the mean length of the carrots using Gro‐Haut in the following circumstances: a) Sample size = 35, confidence level = 98%. b) Sample size = 15, confidence level = 90%. c) What would be the minimum sample needed to estimate the population mean of the length of carrots using Gro‐Haut to within 1.5 cm with 99% confidence? Question 4 An automatic puck shooting machine is a device that fires hockey pucks at specified speeds. The machine’s manufacturer, Puck Chuck, constructed the device so that there was little variance in the velocities of the projectiles. For example, if a machine was to be set at a mean output of 85 miles per hour (mph), its standard deviation would remain 4 mph. Assuming that actual speeds of the device are normally distributed, please answer the following questions about a machine set to shoot pucks at 85 mph: a) What is the probability of a puck being shot at speeds in between 77 and 88 mph? b) If Puck Chuck wanted to reset the machine so that only 17 in 1000 pucks would have velocities of less than 75 mph, what would the mean output of the machine be set to? Question 5 Determine the test statistic (Z* or t*) and the p‐value for each of the each of the following situations and determine if they would cause the rejection of the null hypothesis if the confidence level was set at 95% in each case. (Hint: be wary of the sample size): a) Ho: μ ≤ 35.8 g, Ha: μ > 35.8 g, sample mean = 39.1, sample standard deviation = 7, n = 36. b) Ho: μ ≥ 145 km/h, Ha: μ < 145 km/h, sample mean = 138.5, s = 34, n = 42. c) Ho: μ = 2.48 m, Ha: μ ≠ 2.48 m, sample mean = 2.99, s = 0.68, n = 11. d) Ho: μ ≥ 68.0 minutes, Ha: μ < 68.0 minutes, sample mean = 67.3, s = 3.9, n = 28. e) Ho: μ = 22.7 °C, Ha: μ ≠ 22.7 °C, sample mean = 23.4 °C, s = 1.24 °C, n = 32. Question 6 Montreal Alouettes quarterback Anthony Calvillo has passed for over 6000 yards in the 2004 season, becoming only the third player to do so during the regular season in the Canadian Football League. While discussing this exploit one day, a friend of yours claims that Calvillo’s average passing yards per season exceeds 3000. Curious, you collect the data from his 14‐year career and find the following: Year Yards Year Yards 1994 2582 2001 3671 1995 2831 2002 5013 1996 2571 2003 5891 1997 2177 2004 6041 1998 1526 2005 5556 1999 2592 2006 4714 2000 4277 2007 3608 Please conduct a complete hypothesis test to determine if Anthony Calvillo’s passing performance in a given season does indeed exceed 3000 yards. Conduct this test at the 97.5% confidence level and determine the p‐value. (Hints: Follow the steps for hypothesis testing. Treat the values as a sample since Calvillo’s career has not ended.) Question 7 Socially conscious investors screen out stocks from alcohol and tobacco companies in favour of more “socially conscious” enterprises. One popular measure of stock value is the P/E ratio (price to earnings ratio), with a high P/E indicating that the stock might be overpriced (pay more for less earnings). The stock index of all major stocks has a mean P/E ratio of 19.4. A random sample of 36 “socially conscious” stocks gave a P/E ratio of 17.9 with a standard deviation of 5.2. Determine, with 95% confidence, if the stocks from “socially conscious” companies are different from the mean P/E ratio of all other major stocks. Please conduct a complete hypothesis test and find the p‐value. ...
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