1 A data set includes 40 pulse rates of men and those pulse

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

Solution

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]