Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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• 1 month ago

#I.  The sum (done in my head) is 43.8.  So the mean is

43.8/11 = 3.98 hours.  Calculate the standard deviation by finding the sum of the squared differences

(0.58)^2 + (1.48)^2 + (0.82)^2 + ... + (0.02)^2,

and then dividing by 10 (which is "n-1") and taking the square root.  I'm not going to do this, but let's suppose hypothetically that your standard deviation comes out to s = 0.7.

Then the standard error of the mean is s/sqrt(n), which in my hypothetical case would be 0.7/sqrt(11) = 0.211.  The "t" statistic for the bounds on a 95% confidence interval with 10 degrees of freedom are +/-2.228.  The confidence interval would then be from 3.98-2.228*0.211 to 3.98+2.228*0.211.

So now you just have to go back and do those 11 squared differences and replace my 0.7 and 0.211 with something else.

#II.  It should be obvious that 3.98 hours is not significantly different from 4 hours.  Doesn't take any statistics to see that...