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Confidence Interval for Sample of Size n = 1 When a manned NASA spacecraft lands on Mars, the astronauts encounter a single adult Martian, who is found to be 12.0 ft tall. It is reasonable to assume that the heights of all Martians are normally distributed.
a. The methods of this chapter require information about the variation of a variable. If only one sample value is available, can it give us any information about the variation of the variable?
b. Based on the article “An Effective Confidence Interval for the Mean with Samples of Size One and Two,” by Wall, Boen, and Tweedie (American Statistician, Vol. 55, No. 2), a 95% confidence interval for μ can be found (using methods not discussed in this book) for a sample of size n = 1 randomly selected from a normally distributed population, and it can be expressed as
Use this result to construct a 95% confidence interval using the single sample value of 12.0 ft, and express it in the format of
Based on the result, is it likely that some other randomly selected Martian might be 50 ft tall?
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