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dlinn [17]
3 years ago
11

A research team is testing whether a fuel aditive increases a car's gas mileage. The maker of the additive claims that the addit

ive 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?
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0

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

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

         P( Z

=>  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

 

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