Answer:
No these these result do not differ at 95% confidence level
Step-by-step explanation:
From the question we are told that
The first concentrations is ![c _1= 30.0 \ g/m^3](https://tex.z-dn.net/?f=c%20_1%3D%2030.0%20%5C%20g%2Fm%5E3)
The second concentrations is ![c _2 = 52.9 \ g/m^3](https://tex.z-dn.net/?f=c%20_2%20%3D%2052.9%20%5C%20g%2Fm%5E3)
The first sample size is ![n_1 = 32](https://tex.z-dn.net/?f=n_1%20%3D%20%2032)
The second sample size is ![n_2 = 32](https://tex.z-dn.net/?f=n_2%20%3D%20%2032)
The first standard deviation is ![\sigma_1 = 30.0](https://tex.z-dn.net/?f=%5Csigma_1%20%3D%20%2030.0%20)
The first standard deviation is ![\sigma_1 = 29.0](https://tex.z-dn.net/?f=%5Csigma_1%20%3D%20%2029.0%20)
The mean for Turnpike is ![\= x _1 = \frac{c_1}{n} = \frac{31.4}{32} = 0.98125](https://tex.z-dn.net/?f=%5C%3D%20x%20_1%20%3D%20%5Cfrac%7Bc_1%7D%7Bn%7D%20%20%3D%20%20%5Cfrac%7B31.4%7D%7B32%7D%20%3D%200.98125)
The mean for Tunnel is ![\= x _2 = \frac{c_2}{n} = \frac{52.9}{32} = 1.6531](https://tex.z-dn.net/?f=%5C%3D%20x%20_2%20%3D%20%5Cfrac%7Bc_2%7D%7Bn%7D%20%20%3D%20%20%5Cfrac%7B52.9%7D%7B32%7D%20%3D%201.6531)
The null hypothesis is ![H_o : \mu _1 - \mu_2 = 0](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu%20_1%20-%20%5Cmu_2%20%20%3D%20%200)
The alternative hypothesis is ![H_a : \mu _1 - \mu_2 \ne 0](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20%5Cmu%20_1%20-%20%5Cmu_2%20%20%5Cne%20%200)
Generally the test statistics is mathematically represented as
![t = \frac{\= x_1 - \= x_2}{ \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }}](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B%5C%3D%20x_1%20-%20%5C%3D%20x_2%7D%7B%20%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%20%20%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%20%7D%7D)
![t = \frac{0.98125 - 1.6531}{ \sqrt{\frac{30^2}{32} +\frac{29^2}{32} }}](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B0.98125%20-%201.6531%7D%7B%20%5Csqrt%7B%5Cfrac%7B30%5E2%7D%7B32%7D%20%20%2B%5Cfrac%7B29%5E2%7D%7B32%7D%20%7D%7D)
![t = - 0.0899](https://tex.z-dn.net/?f=t%20%3D%20-%200.0899)
Generally the degree of freedom is mathematically represented as
![df = 32+ 32 - 2](https://tex.z-dn.net/?f=df%20%3D%20%2032%2B%2032%20-%202)
![df = 62](https://tex.z-dn.net/?f=df%20%3D%20%2062)
The significance
is evaluated as
![\alpha = (C - 100 )\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20%28C%20-%20100%20%29%5C%25)
=> ![\alpha = (95 - 100 )\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20%2895%20-%20100%20%29%5C%25)
=> ![\alpha =0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D0.05)
The critical value is evaluated as
![t_c = 2 * t_{0.05 , 62}](https://tex.z-dn.net/?f=t_c%20%20%3D%20%202%20%20%2A%20%20t_%7B0.05%20%2C%20%2062%7D)
From the student t- distribution table
![t_{0.05, 62} = 1.67](https://tex.z-dn.net/?f=t_%7B0.05%2C%2062%7D%20%3D%20%201.67)
So
![t_c = 2 * 1.67](https://tex.z-dn.net/?f=t_c%20%20%3D%20%202%20%2A%201.67)
=> ![t_c = 3.34](https://tex.z-dn.net/?f=t_c%20%20%3D%203.34)
given that
we fail to reject the null hypothesis so this mean that the result do not differ