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 we have used 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? (What if the data is not
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
a. The methods we have used 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? (What if the data is not normal?)
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 for a sample of size n = 1 randomly selected from a normally distributed population, and it can be expressed as x ± 9.68*|x|.
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 x – E < µ < x + E.
Based on the result, is it likely that some other randomly selected Martian might be 50 ft tall?
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