Confidence Interval for Sample of Size n 5 1 When a lone alien lands on earth, he is measured and is found to have a height of 3.2 ft. It is reasonable to expect that the height of all such aliens 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. When using the methods of this section, what happens when you try to use the single height in constructing a 95% confidence interval?

c. Based on the article “An Effective Confidence Interval for the Mean with Samples of Size One and Two” (by Wall, Boen, and Tweedie, The American Statistician, Vol. 55, No. 2), a 95% confidence interval for m can be found (using methods not discussed in this book) for a sample of size n 5 1 randomly selected from a normally distributed population, and it can be expressed as x  9.68 . Use this result to construct a 95% confidence interval using the single sample value of 3.2 ft, and express it in the format of . Based on the result, is it likely that some other randomly selected alien might be 50 ft tall?