When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis. Use α= 0.05 significance level to test the claim that in Dublin, car ages and taxi ages have the same variation. Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8
Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

The  Decision Rule

Fail to reject the null hypothesis

The conclusion

 There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

Step-by-step explanation:

From the question we are told that

   The data is  

      Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8

     Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

      The  level of significance

 Generally the null hypothesis  is  

                  the alternative hypothesis is  

Generally the sample mean for the age of  cars is mathematically represented as

=>    

=>    

Generally the standard deviation of age of  cars

=>  

=>  

Generally the sample mean for the age of taxi is mathematically represented as

=>    

=>    

Generally the standard deviation of age of  taxi

=>  

=>  

Generally the test statistics is mathematically represented as

=>  

=>  

Generally the degree of freedom is mathematically  represented as

From the t distribution table  the at the obtained degree of freedom = 45 is  

So  the  p-value  is

From the obtained values we see that the  p-value  >   hence we fail to reject the null hypothesis

Hence the there is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi