Question

A research team is testing whether a fuel aditive increases a car's gas mileage. The maker of the additive claims that the additive will increase a car's gas mileage by at least 6 mpg. Among 25 cars that were treated with the additive, the average increase in mileage was 5.3 mpg with a standard deviation of 1.8 mpg. The research team found the z-score to be -1.94. Is there enough evidence to reject the company's evidence?

Answer 1

Answer:

Yes  there is sufficient evidence to  reject the company's evidence

Step-by-step explanation:

From the question we are told that  

   The sample size is  n =  25

    The mean is  $\= x = 5.3 \ mpg$

     The standard deviation is  $\sigma = 1.8 \ mpg$

    The z-score is  z = -1.94

The null hypothesis is  $H_o : \mu = 6 \ mpg$

The alternative hypothesis is  $H_a : \mu \ne 6$

 Generally the p-value is mathematically evaluated as  

           $p-value = 2 * P( Z <-1.94)$

From the z table  the area under the normal curve to the left corresponding to    -1.94  is

         $P( Z <-1.94) = 0.02619$

=>  $p-value = 2 * 0.02619$

=>  $p-value = 0.052$

Let assume the level of significance is  $\alpha = 0.05$

 Hence the  $p-value > \alpha$ this mean that

   The  decision rule is  

Fail to reject the null hypothesis

The conclusion is

 There is sufficient evidence to  reject the company's evidence