Question
In: Statistics and Probability
The following data are the joint temperatures of the O-rings (oF) for each test firing or...
The following data are the joint temperatures of the O-rings (oF) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131):
| 86 | 45 | 61 | 40 | 83 | 67 | 45 | 66 | 70 | 69 | 80 | 58 | 68 | 60 | 67 | 72 | 73 | 70 | 57 | 63 | 70 | 78 | 52 | 67 | 53 | 67 | 75 | 61 | 70 | 81 | 76 | 79 | 75 | 76 | 58 | 31 |
Round your answers to 2 decimal places (e.g. 98.76).
(a) Using the entire data, calculate the sample mean and sample standard deviation.
Sample mean =
Sample standard deviation =
(b) Remove the smallest observation (31°F) and calculate the sample mean and sample standard deviation of the remaining data.
Sample mean =
Sample standard deviation =
(c) With the smallest observation removed:
the sample mean Choose your answer; the sample mean ____ and the sample standard deviation Choose your answer; the sample standard deviation ______
Solutions
Expert Solution
a. Sample mean is 
Create the following table.
| data | data-mean | (data - mean)2 |
| 86 | 20.1944 | 407.81379136 |
| 45 | -20.8056 | 432.87299136 |
| 61 | -4.8056 | 23.09379136 |
| 40 | -25.8056 | 665.92899136 |
| 83 | 17.1944 | 295.64739136 |
| 67 | 1.1944 | 1.42659136 |
| 45 | -20.8056 | 432.87299136 |
| 66 | 0.1944 | 0.037791360000001 |
| 70 | 4.1944 | 17.59299136 |
| 69 | 3.1944 | 10.20419136 |
| 80 | 14.1944 | 201.48099136 |
| 58 | -7.8056 | 60.92739136 |
| 68 | 2.1944 | 4.81539136 |
| 60 | -5.8056 | 33.70499136 |
| 67 | 1.1944 | 1.42659136 |
| 72 | 6.1944 | 38.37059136 |
| 73 | 7.1944 | 51.75939136 |
| 70 | 4.1944 | 17.59299136 |
| 57 | -8.8056 | 77.53859136 |
| 63 | -2.8056 | 7.87139136 |
| 70 | 4.1944 | 17.59299136 |
| 78 | 12.1944 | 148.70339136 |
| 52 | -13.8056 | 190.59459136 |
| 67 | 1.1944 | 1.42659136 |
| 53 | -12.8056 | 163.98339136 |
| 67 | 1.1944 | 1.42659136 |
| 75 | 9.1944 | 84.53699136 |
| 61 | -4.8056 | 23.09379136 |
| 70 | 4.1944 | 17.59299136 |
| 81 | 15.1944 | 230.86979136 |
| 76 | 10.1944 | 103.92579136 |
| 79 | 13.1944 | 174.09219136 |
| 75 | 9.1944 | 84.53699136 |
| 76 | 10.1944 | 103.92579136 |
| 58 | -7.8056 | 60.92739136 |
| 31 | -34.8056 | 1211.42979136 |
Find the sum of numbers in the last column to get. 
So standard deviation is 
b. Removing 31, we get sample mean as 
Create the following table.
| data | data-mean | (data - mean)2 |
| 86 | 19.2 | 368.64 |
| 45 | -21.8 | 475.24 |
| 61 | -5.8 | 33.64 |
| 40 | -26.8 | 718.24 |
| 83 | 16.2 | 262.44 |
| 67 | 0.2 | 0.040000000000001 |
| 45 | -21.8 | 475.24 |
| 66 | -0.8 | 0.64 |
| 70 | 3.2 | 10.24 |
| 69 | 2.2 | 4.84 |
| 80 | 13.2 | 174.24 |
| 58 | -8.8 | 77.44 |
| 68 | 1.2 | 1.44 |
| 60 | -6.8 | 46.24 |
| 67 | 0.2 | 0.040000000000001 |
| 72 | 5.2 | 27.04 |
| 73 | 6.2 | 38.44 |
| 70 | 3.2 | 10.24 |
| 57 | -9.8 | 96.04 |
| 63 | -3.8 | 14.44 |
| 70 | 3.2 | 10.24 |
| 78 | 11.2 | 125.44 |
| 52 | -14.8 | 219.04 |
| 67 | 0.2 | 0.040000000000001 |
| 53 | -13.8 | 190.44 |
| 67 | 0.2 | 0.040000000000001 |
| 75 | 8.2 | 67.24 |
| 61 | -5.8 | 33.64 |
| 70 | 3.2 | 10.24 |
| 81 | 14.2 | 201.64 |
| 76 | 9.2 | 84.64 |
| 79 | 12.2 | 148.84 |
| 75 | 8.2 | 67.24 |
| 76 | 9.2 | 84.64 |
| 58 | -8.8 | 77.44 |
Find the sum of numbers in the last column to get. 
So standard deviation is 
c. With the smallest observation removed: the sample mean increased and the sample standard deviation decreased.
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