Please help with explanation Thank you 9 10 points In a samp

Please help with explanation. Thank you

9. (10 points) In a sample of 40 men it was found that they had a mean pulse rate was 67.3 beats per minute and a standard deviation of 10.3 beats per minute. In a sample of 40 women it was found that they had a mean pulse rate was 77.5 beats per minute and a standard deviation of 11.6 beats per minute. a. Construct a 99% confidence interval estimate (show work) of the standard deviation of the pulse rates of men. b. Construct a 99% confidence interval estimate (show work) of the standard deviation of the pulse rates of women. e. Compare the variation of the pulse rates of men and women. Does there appear to be a difference?

Solution

A)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    67.3          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    10.3          
n = sample size =    40          
              
Thus,              
Margin of Error E =    4.194926043          
Lower bound =    63.10507396          
Upper bound =    71.49492604          
              
Thus, the confidence interval is              
              
(   63.10507396   ,   71.49492604   ) [ANSWER]

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    77.5          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    11.6          
n = sample size =    40          
              
Thus,              
Margin of Error E =    4.724382729          
Lower bound =    72.77561727          
Upper bound =    82.22438273          
              
Thus, the confidence interval is              
              
(   72.77561727   ,   82.22438273   ) [ANSWER]

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c)

YES, THERE APPEARS TO BE A DIFFERENCE, because the two intervals did not overlap.