GSB 420 Prof. Jin Choi Homework on Confidence Interval Construction This homework has a total of 10 points. Name: _____________________________________ According to the Wall Street Journal article shown below, the average January temperature for the 48 contiguous states for the 1895-2013 period is 30.63 degrees in Fahrenheit. 1. If the population standard error of the average January temperature during this period is 2.2 degrees in F, what is the 95% confidence interval for the average January temperature? (3 points) 2. Consider that an average January temperature is normal if it falls within the 95% confidence interval constructed above in (1). If so, an average January temperature of 35 degrees in Fahrenheit be considered "abnormal"? Justify your answer. (3 points) 3. Suppose that you take a sample of 10 average February temperatures from this 18952013 period and found their average to be 40 and sample standard error to be 2.5 degrees in Fahrenheit. Based on this information, construct the 99% confidence interval for the average February temperature. (4 points) HTTP://ONLINE.WSJ.COM/NEWS/ARTICLES/SB10001424052702303743604579355184004388274 U.S. NEWS Now Is the Winter of Our Discontent Weather Experts Blame Oceanic Quirk for Extreme Cold and Unusual Warmth Across U.S. By ROBERT LEE HOTZ Jan. 31, 2014 7:11 p.m. ET Chicago at times in January was colder than the South Pole as extreme weather gripped much of the U.S. Here, the frozen shore of Lake Michigan. Getty Images At times in January, Chicago was colder than the South Pole, while flowers bloomed out of season in balmy Juneau, Alaska. Driven by contorted bends of the jet stream, cold snaps and snow kept Northern and Southern states in a deep freeze, while unusually warm weather and record drought gripped the far West. The U.S. has been a country divided by temperature extremes, in a winter of record Western highs and bone-chilling Eastern lows, federal climate experts and private meteorologists said. A formal federal tally of January's temperature trends won't be completed for weeks, but preliminary regional data compiled by commercial meteorologists suggest that the Eastern half of the country is experiencing one of its 10 coldest winters on recordwith thousands of local records for cold already tied or broken. By contrast, California, Alaska and the Western U.S. are having one of the 10 warmest winters, with several cities setting records in January for high temperatures. "We are talking about significant departures from normal," said meteorologist Joe D'Aleo, chief forecaster at Weatherbell Analytics LLC, a commercial forecasting company based in New York. Weather experts blame it all on a vast pool of warm water in the North Pacificup to seven degrees hotter than in most years. Generating a plume of rising hot air, it has pushed the polar jet stream, which steers air across the continent from west to east, further north and then south in a series of kinks like accordion pleats. The same odd continental pattern of air circulation contributed to the coldest U.S. winters on record in 1977 and 1979, experts said. "The jet stream has configured itself in a way that it is positioned to bring warm air to the West and shots of really cold air to the East," said Deke Arndt, chief of climate monitoring at the National Climatic Data Center in Asheville, N.C. As a consequence, the Western half of the country has been almost as much above average as the Eastern half has been below average. "If you average the extremes, you miss out on how truly extraordinary the weather this January is," said Jeff Masters, chief meteorologist at Weather Underground, a commercial forecasting service. The month unofficially edged out 1948 as only the 25th coldest U.S. January, based on more than a century of record-keeping. "The bitter cold we experienced in January was certainly unusual and the coldest we have seen in the 21st century, said Dr. Arndt. "But they were the kinds of temperatures we would routinely see in two out of three winters in the cold decades of the 1970s and 1990s." Even so, it has been cold enough to drive the penguins indoors at the National Aviary in Pittsburgh, icy enough to freeze over much of the Great Lakes, and snowy enough that airlines in January canceled more than 36,000 flights. By a preliminary count, the month set more than a thousand local records for snowfall. January was so cold that in Chicago, left, it got colder than the South Pole, right. Left: Scott Olson/Getty Images; Right: Associated Press At the same time, it was warm and dry enough in the West that California's snowpack is now at its lowest level in 50 years, threatening the state's water supply. Temperatures in January topped 88 degrees in Long Beach, while Anchorage, Alaska, notched its warmest January day on record this past Monday, with temperatures southwest of the city reaching 62 degrees. "It is a study in extremes," Dr. Masters said. Write to Robert Lee Hotz at sciencejournal@wsj.com