1. A data set includes 40 pulse rates of men, and those pulse rates have a mean
ID: 3378954 • Letter: 1
Question
1. A data set includes 40 pulse rates of men, and those pulse rates have a mean of 67.3 beats per minute and a standard deviation of 10.3 beats per minute. Construct a 99% confidence interval estimate of the standard deviation of the pulse rates of men. multiple choice
8.4 beats per minute < <11.2 beats per minute
6.3 beats per minute < <16.6 beats per minute
9.7 beats per minute < <10.5 beats per minute
7.9 beats per minute < <14.1 beats per minute
5.8 beats per minute < <12.1 beats per minute
8.4 beats per minute < <11.2 beats per minute
6.3 beats per minute < <16.6 beats per minute
9.7 beats per minute < <10.5 beats per minute
7.9 beats per minute < <14.1 beats per minute
5.8 beats per minute < <12.1 beats per minute
Explanation / Answer
As
df = n - 1 = 39
alpha = (1 - confidence level)/2 = 0.005
Then the critical values for chi^2 are
chi^2(alpha/2) = 65.4755709
chi^2(alpha/2) = 19.99586787
Thus, as
lower bound = (n - 1) s^2 / chi^2(alpha/2) = 63.19165977
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) = 206.9182506
Thus, the confidence interval for the variance is
( 63.19165977 , 206.9182506 )
Also, for the standard deviation, getting the square root of the bounds,
( 7.9 , 14.1 ) [ANSWER, OPTION D]
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