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First picture is the question and its answer key:

enter image description here

The second picture is my solution:

enter image description here

I know that $S^2=\frac{\sum(x_i-\bar x)^2}{n-1}$

But in the answer key, $s^2$ cannot be found in that way. I guess, there is a mistake here. Or, ıs there a rule that I dont know?

Please clarify this. Thank you.

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5
  • $\begingroup$ You should be calculating $s^2$ around a "mean" of zero, not of 4.57. 4.57 is the average distance from the target; for an accuracy of this type, you want to know the standard deviation of where the missile hits around the target, not the standard deviation around the average distance from the target. $\endgroup$
    – jbowman
    Commented Apr 21, 2014 at 17:29
  • 1
    $\begingroup$ The answer is blatantly wrong on three counts. (1) Even under simplistic assumptions about the targeting errors (namely, that they are approximately Normal and do not favor any particular direction over any other), the degrees of freedom will not be $6$! They will be either $14$ or $21$ depending on whether errors are computed in two or three dimensions. (2) Even with $6$ df the rejection region would not extend all the way to $164$--it only goes to $12.6$. (3) Worse, this is the wrong rejection region! "Strong evidence" would be a significantly small (not large) value. Throw this book away! $\endgroup$
    – whuber ♦
    Commented Apr 21, 2014 at 17:48
  • $\begingroup$ As a result, my solution is true, Isnt it? @whuber $\endgroup$
    – 1190
    Commented Apr 21, 2014 at 18:36
  • $\begingroup$ I'm sorry, it's not: please read @jbowman's comment. $\endgroup$
    – whuber ♦
    Commented Apr 21, 2014 at 18:47
  • $\begingroup$ @whuber - I wish I could give you a lot more than 1 +1 for that "blatantly wrong" comment! $\endgroup$
    – jbowman
    Commented Apr 22, 2014 at 17:24

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