Business Statistics Homework #4, Fall 2011 Instructions: For all problems, use the 7 Steps in Hypothesis testing and round all z and t- values to 2 decimal places. (CNN) -- An asteroid the size of an aircraft carrier will pass Earth within eight-tenths of the distance of the moon Tuesday (11/8/11), the closest approach to Earth of an object this size in more than 30 years. The closest approach will occur at 6:28 p.m. ET when the asteroid passes within 202,000 miles of our planet, NASA said. The space agency classified the asteroid as a "potentially hazardous object." If the asteroid were to crash into Earth, it could cause a 4,000 megaton blast and a magnitude 7.0 earthquake, according to scientists at Purdue University. If it fell into the ocean, it could cause a 70-foot high tsunami within 60 miles of the crash site, the experts said. However, the space rock, called Asteroid 2005 YU55, poses no threat of an Earth collision, according to NASA's Near Earth Object Program. Scientists claim that if an asteroid comes within 197,000 miles to the earth, the asteroid is considered a potential threat. Scientists reconstructed the shape of the asteroid with a resolution as fine as 13 feet (4 meters) using the antennas. The scientists test the possibility that the asteroid was a potential threat to Earth by performing 173 sample simulations. The mean distance from the earth was 198,000 miles with a standard deviation of 7,783 miles. a) Using, can you concluded that the Asteroid 2005 YU55 is a potential threat to earth? b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error?
Billboard.biz--Concertgoers sick of ballooning ticket prices should have some extra pocket change to rattle with their rock 'n' roll in the New Year. 2010 was tough for the concert business as high prices kept many fans at home. Promoters now say they plan to make shows more affordable in 2011. ABC 20/20--A ticket to a Rolling Stones concert cost about $8 in 1969. Today, it can cost you up to $350 to get into a Stones show. Prices of concert tickets are rising faster and higher than those for movies, theater even sporting events. But rock 'n' roll is supposed to be the antiestablishment art form, and maybe that's why so many fans feel aggravated that rock once for the masses is now often for only the rich. Receiving mixed information on the trend for an average price of a concert ticket for 2011, you decide to do your own research. Using a sample of 57 concert ticket prices, you find an average ticket price of $49.69 with a standard deviation of $5.31. Does the data support Billboard.biz s claim that the price of concert tickets for 2011 are lower than the 2010 average price of $51? Use
Los Angeles Time More than an entire day -- that's how long children sit in front of the television in an average week, according to new findings released Monday by Nielsen. The amount of television usage by children reached an eight-year high, with kids ages 2 to 5 watching the screen for more than 32 hours a week on average and those ages 6 to 11 watching more than 28 hours a week. Kids ages 2 to 5 spent an average of 3 hours and 47 minutes a day watching television, up from 3 hours and 40 minutes in the previous year, according to Nielsen. Older children watched an average of 3 hours and 20 minutes a day, up from 3 hours and 17 minutes. Researchers claim that television watching is up from 3 hours and 40 minutes per day for children ages 2 to 5, and up from 3 hours and 17 minutes a day for children ages 6 to 11. Assuming the samples are normally distributed and a sample of 24 children from the ages of 2 to 5 with a standard deviation of 38 minutes was studied along with a sample of 27 children from the ages 6 to 11 with a standard deviation of 33 minutes. Convert all the times to minutes. a) Can the researchers claim that television watching for kids ages 2 to 5 has increased from the previous year? (Assume ) b) Can the researchers claim that television watching for kids ages 6 to 11 has increased from the previous year? (Assume ) c) After analyzing more data, researchers believe there is also a relation between the age of the child and the amount of television he or she watches. A sample of 42 kids from the age of 2 to 5 resulted in a standard deviation of 43 minutes and an average of 3 hours and 35 minutes. Similarly, a sample of 54 kids from the ages of 6 to 11 resulted in a standard deviation of 35 minutes and an average of 3 hours and 18 minutes. Test if 6 to 11 year olds watch less TV than 2 to 5 year olds. (Assume )
MADE HOW.com-- An official Major League baseball consists of a round cushioned cork center called a "pill," wrapped tightly in windings of wool and polyester/cotton yarn, and covered by stitched cowhide. Approximately 600,000 baseballs are used by all Major League teams combined during the course of a season. The average baseball remains in play for only five to seven pitches in a Major League game. Each ball must weigh between 5 and 5.25 ounces (141.75-148.83 grams) and measure between 9 and 9.25 inches (22.86-23.49 centimeters) in circumference to conform to Major League standards. A statistically representative sample of each shipment of baseballs is tested to measure Co- Efficient Of Restitution (COR), using Major League Baseball's officially sanctioned testing procedures. Essentially, the COR is an indication of the resiliency of a baseball. The COR test involves shooting a baseball from an air cannon at a velocity of 85-feet-a-second (25.90-meters-a-second) at a wooden wall from a distance of eight feet (2.43 meters), and measuring the speed with which the ball rebounds off the wall. Major League COR specifications stipulate that a baseball must rebound at 54.6 percent of the initial velocity. Therefore, in order for a baseball to be used by the MLB the baseball must rebound off the wall 46.41 feet. In a shipment of 1,200 baseballs to Loper Sports, a sample of 99 baseballs was tested to see if the baseballs fulfilled the above specifications. The average rebound was 45.71 feet with a standard deviation of 4.12 feet. Should Loper Sports keep the shipment or return the baseballs to the manufacturer? Interpret your results with 95% confidence. Interpret your results with 99% confidence.
FoxNews-- Pediatricians write more than 10 million unnecessary antibiotic prescriptions for conditions like the flu and asthma every year, suggests a new study. Those ailments, and others not caused by bacteria, don't respond to the drugs. But misuse of antibiotics contributes to drug resistance so those same medications might not work in the future when they're really needed. The new study involved a nationally-representative sample of 65,000 outpatient visits by kids under 18 in 2006 through 2008. Using medical codes, researchers were able to determine the type of diagnosis kids were given, as well as what kind of drugs, if any, they were prescribed. In total, doctors prescribed an antibiotic at one in every five visits. Most prescriptions were given out for kids with respiratory ailments, including sinus infections and pneumonia. Some of those infections are caused by bacteria, and antibiotics are warranted. But, almost one-quarter of all antibiotic prescriptions were given to kids with respiratory conditions that probably or definitely do not call for antibiotics. This shows that over 5% of patients that visit a hospital are given a prescription that is unnecessary. A survey of 43 patients was taken in Kearney to see if this claim holds true that patients are being given unnecessary prescriptions. Out of the 43 patients, 4 were given unnecessary prescriptions. a) Using and the steps in hypothesis testing, what conclusion would be made? b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error?
USMCvietnam.net--The Silent Drill Platoon first performed in 1948, originally as a one-time show, and received such an overwhelming response that it soon became part of the routine parades at Marine Barracks, Washington, D.C. Marines are selected from students at the two Schools of Infantry, located at Camp Pendleton, California, and Camp Lejeune, North Carolina, from interviews conducted by barracks personnel. Once selected, Marines are assigned to Marine Barracks, Washington, D.C., to serve a two-year ceremonial tour. Beyond their ceremonial duties, the Marines collaterally train in the field as infantrymen. Throughout the year, these Marines hone their infantry skills at the Marine Corps Combat Development Command in Marine Corps Base Quantico, Virginia and other bases. The Marines selected must be male and must be between 5'11" and 6'1" tall and be in the median of their weight requirements for their height. Uniformity is a key asset. In the past, around 22% of the Marine Corps members fell into these requirements. Since then individuals average height and weight have been changing. The Marine Corps decided to take a sample of marines located at Camp Pendleton to see if the above percentage still holds true. 103 marines were weighed and measured for their height. Out of the 103 marines, only 21 of the marines met the height and weight requirements to fit the uniformity of the Silent Drill Platoon. Can you conclude that the proportion of marines that meet the standards of the Silent Drill Platoon has not changed from previous years? Interpret results with 80% confidence.
USA Today Cell phones are becoming the only home phones in an increasing number of U.S. households, a trend intensified by challenging economic conditions, according to a new report released today from the National Center for Health Statistics. More than one in four U.S. homes, or 26.6%, had only a wireless phone as of June 2010, up from 13.6% in 2007. The percentage of wireless-only homes increased in every state, ranging from 35.2% in Arkansas to 12.8% in Rhode Island and New Jersey. A sample from the Kearney area was taken, to see if this claim held true. Use the table below to determine if fewer people have landline telephones today than they did in 2010. Interpret your results with 95% confidence. Interpret your results with 99% confidence. 2011 2010 Number of people sampled 67 53 Number of people with land lines 51 47
U.S. Airlines vary in numerous ways. Researchers want to determine the factors which cause each airline to have different fleet sizes. In the Excel Spreadsheet Airlines, several U.S. Airlines are listed with the year they were founded and the number of destinations they fly to. Researchers believe that these two characteristics are what help determine the number of planes (fleet size) each airline owns. a) Create an Excel Scatter Graph for each of the data for the columns discussed above. b) Use regression analysis to develop an estimated regression equation that could be used to predict the airline's fleet size given the year in which it was founded. Write the regression equation. Use the 7 steps of hypothesis testing to see if the year in which the airline was founded is significant. c) Use regression analysis to develop an estimated regression equation that could be used to predict the airline's fleet size given the number of destinations the airline flies to. Write the regression equation. Use the 7 steps of hypothesis testing to see if the number of destinations the airline flies to is significant.