Data set
70 69 68 67 73 77 75 68 72 71
71 72 72 72 71 73 67 72 72 78
72 68 65 67 73 77 77 72 72 69
Find the following statistics. If any statistic is not a whole number, round to the nearest hundredth.
n =
x-bar =
sx =
mid-range =
above =
Does the data pass the mean to median test?
Does the data pass the z(mid-range) test?
If it passes both tests, find the 95% confidence interval for mux, and write it as a sentence.
Find the 95% confidence interval for sigmax, and write it as a sentence.
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n = 30
x-bar = 71.4
sx = 3.27
mid-range = 71.5
above = 17
Does the data pass the mean to median test?
n/2 = 15, so the formula is
(17-15)^2/15 = 4/15 = 0.267 < 1.353
Yes, it passes.
Does the data pass the z(mid-range) test?
(71.5-71.4)/3.27 = .03 which is between -.5 and .5, so yes it passes.
If it passes both tests, find the 95% confidence interval for mux, and write it as a sentence.
n = 30, d.f. = 30 - 1 = 29, so the CLM_95% = 2.045
71.4 - 2.045*3.27/sqrt(30) = 70.18
71.4 + 2.045*3.27/sqrt(30) = 72.62
Given this set of 30 subjects, we are 95% confident that the average of the underlying population for this variable is between 70.18 and 72.62.
Find the 95% confidence interval for sigmax, and write it as a sentence.
Again d.f. = 29, so chi^2_R = 45.722 and chi^2_L = 16.047
sqrt(3.27^2*29/45.722) = 2.61
sqrt(3.27^2*29/16.047) = 4.40
Given this set of 30 subjects, we are 95% confident that the standard deviation of the underlying population for this variable is between 2.61 and 4.40.
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