4. Hydrocarbons in the cab of an automobile were measured during trips on the New Jersey Turnpike and trips through the Lincoln Tunnel connecting New York and New Jersey. The concentrations (± standard deviations) of m- and p-xylene were: Turnpike: 31.4 ± 30.0 g/m3 (32 measurements) Tunnel: 52.9 ± 29.8 g/m3 (32 measurements) Do these results differ at the 95% confidence level?

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  

      The second concentrations is  

  The first sample size is  

    The second sample size is  

   The  first standard deviation is

     The  first standard deviation is

The mean for  Turnpike is  

The mean for   Tunnel is  

The  null hypothesis is  

The  alternative hypothesis is  

Generally the test statistics is mathematically represented as

Generally the degree of freedom is mathematically represented as

The  significance  is  evaluated as

=>  

=>  

The  critical value  is evaluated as

From the student t- distribution table  

So

=>  

given that

        we fail to reject the null hypothesis so  this mean that the result do  not differ

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

step-by-step explanation: 4 cause 2+2=4