Question

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) 84, 49, 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. Set aside the smallest observation (31oF) and re-compute the sample mean and sample standard deviation. Note the difference from the answers in part 1. Round your answers to 2 decimal places.

Answer 1

Sample mean = 65.86

Sample standard deviation, s = 12.16

Explanation:

We are given the following in the question:

84, 49, 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

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`\bar{x} =\displaystyle(2371)/(36) = 65.86`

Sum of squares of differences = 5174.30

`s = \sqrt{(5174.30)/(35)} = 12.16`