See attached file.
I am sure many of you remember the fateful event that occurred in 1986 with the Space Shuttle Challenger disaster. I still remember where I was at the time of the explosion. There was much debate between NASA officials, Morton Thiokol (MT) Management (contractors that built the Challenger rocket boosters) and Morton Thiokol Engineers in regards to the ability of the Challenger fitness to fly. The engineers did not want the Challenger to go into space due to uncertainty of a mechanical design defect. The design defect was highly sensitive to temperature. The temperature at the time of launch (29 degrees F) could cause the Shuttle rocket boosters to fail, thus leading to an explosion.
On the eve of the launch, an emergency teleconference had been called between NASA and Morton Thiokol Corporation, the contractor that provided solid rocket motors for the shuttle. At the teleconference, a group of Thiokol engineers (Led by Roger Biosjoly) had pleaded with their superiors and NASA to delay the launch. They feared that the cold temperatures would cause a failure in synthetic rubber O-rings that sealed joints in the rocket motor. If the rings failed, the motor could blow up. The engineers recommended strongly that NASA wait for warmer weather. But Thiokol and NASA both faced strong pressure to get the shuttle in the air (Bolman and Deal, 1997).
A NASA manager appalled by the recommendation to halt the flight said: "My God, Thiokol when do you want me to launch? Next April?" (McConnell, 1987, p. 196)
Thiokol had gained the lucrative sole source contract for the solid rocket boosters 13 years earlier, during a bitterly disputed award process characterized by some veteran observers as a low point in squalid political intrigue. At the time of the award to then relatively small Thiokol Chemical Company in Brigham Utah, both newly appointed chairman of the Senate Aeronautics and Space Science Committee, Democratic Senator Frank Moss, and new NASA administrator, Dr. James Fletcher, were both insiders in the tightly knit Utah political hierarchy.
By Summer 1985, however, Thiokol's monopoly position was under attack and the corporations executive were afraid to risk their billion-dollar contract by halting shuttle flight operations long enough to correct flaws in the booster joint design (McConnell, 1987, p. 7).
US (Bolman & Deal, 1997) budget deficit was soaring. Managers at NASA were experiencing pressures of their own. As part of their effort to build congressional support for the space program, NASA had promised that the shuttle would eventually pay for itself in cargo fees, like a boxcar in space. The projections of profitability were based on a very ambitious plan: 12 flights in 1984, 14 in 1985 and 17 in 1986. NASA had fallen very behind in schedule: 5 launches in 1984, and 8 in 1985. The promise of "routine access to space" and flights that would pay for themselves looked more and more dubious. With every flight costing the taxpayers about $100 million, NASA needed a lot of money from Congress, but the prospects were getting bleaker. NASA's credibility was eroding while the budget deficit was growing!
The temperature on the day of the launch was to be 29 degrees F at 9 am. Extremely cold for the rocket booster O-rings. The MT engineers said that the O-ring temperature must be greater than 53 degrees F to ensure a safe flight (or at least reduce the risk of an explosion). NASA and MT management disagreed due to the lack of evidence and uncertainty that the boosters would blow since this had never occurred in the past. However, Shuttle launches had never occurred in temperatures below 53 degrees and the freezing cold weather could cause the rubber O-rings not to seal, allowing fuel to shoot out of the booster. The temperature for the previous (n) 7 flights that year were:
Flight 1 65 degrees
Flight 2 71 degrees
Flight 3 68 degrees
Flight 4 74 degrees
Flight 5 74 degrees
Flight 6 61 degrees
Flight 7 83 degrees
At a 95% confidence level. Determine if the MT engineers hypothesis was correct. Note, you cannot use the Z-table for this problem. You must use the "student's T distribution table". You can find this table in course material room.
Step by step method for computing test statistic for one sample t test for Space Shuttle Challenger data set.