Answer:
Yes there is a significant difference in the standard deviations of the two sets of measurements made by the two instruments at the 95%
![F_{calc} = 8.3457](https://tex.z-dn.net/?f=F_%7Bcalc%7D%20%3D%208.3457)
Step-by-step explanation:
From the question we are told that
The normal bicarbonate level is k = 23-29 mmol/L
The number of times the blood was tested is n = 6
The mean concentration for old instrument is
The standard deviation is ![\sigma_1 = 1.56\ mmol/L](https://tex.z-dn.net/?f=%5Csigma_1%20%3D%20%201.56%5C%20mmol%2FL)
The mean concentration for the new instrument is ![\= x_2 = 25.9 mmol/L](https://tex.z-dn.net/?f=%5C%3D%20x_2%20%3D%20%2025.9%20mmol%2FL)
The standard deviation is ![\sigma_2 = 0.54 mmol/L](https://tex.z-dn.net/?f=%5Csigma_2%20%20%3D%20%200.54%20mmol%2FL)
The confidence level is 95%
The level of significance is mathematically represented as ![\alpha = (100 - 95)\%](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%20%28100%20-%2095%29%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.05)
Generally the test statistics is mathematically represented as
![F_{calc} = \frac{\sigma_1 ^2}{\sigma_2^2}](https://tex.z-dn.net/?f=F_%7Bcalc%7D%20%3D%20%20%5Cfrac%7B%5Csigma_1%20%5E2%7D%7B%5Csigma_2%5E2%7D)
=> ![F_{calc} = \frac{1.56^2}{0.54^2}](https://tex.z-dn.net/?f=F_%7Bcalc%7D%20%3D%20%20%5Cfrac%7B1.56%5E2%7D%7B0.54%5E2%7D)
=> ![F_{calc} = 8.3457](https://tex.z-dn.net/?f=F_%7Bcalc%7D%20%3D%20%208.3457)
Generally the degree of freedom for the old instrument is is mathematically evaluated as
![df = n -1](https://tex.z-dn.net/?f=df%20%3D%20%20n%20-1)
=>
=>
Generally the degree of freedom for the new instrument is is mathematically evaluated as
![df_1 = n -1](https://tex.z-dn.net/?f=df_1%20%3D%20%20n%20-1)
=>
=>
For the f distribution table the critical value of
at df and
is
![F_{tab} =5.0503](https://tex.z-dn.net/?f=F_%7Btab%7D%20%3D5.0503)
Generally given that the
it means that there is a significant difference in the standard deviations of the two sets of measurements made by the two instruments at the 95%