An automobile manufacturer claims that their van has a 46.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van. After testing 140 vans they found a mean MPG of 46.0. Assume the standard deviation is known to be 2.6. Is there sufficient evidence at the 0.02 level that the vans underperform the manufacturer's MPG rating?

The decision rule is  

Fail to reject the null hypothesis

The conclusion

There is no  sufficient evidence to conclude that the vans underperform the manufacturer's MPG rating

Step-by-step explanation:

From the question we are told that

   The population mean is  

    The sample size is  n  =  140

     The sample mean is  

    The standard deviation is  

     The level of significance is  

   The null hypothesis is  

   The alternative hypothesis is

Generally the test statistics is mathematically represented as

=>  

=>  

From the z table  the area under the normal curve to the left corresponding to  

-1.8203 is  

Generally the p-value is mathematically represented as

From the value obtained we see that the p-value >   hence

The decision rule is  

Fail to reject the null hypothesis

The conclusion

There is no  sufficient evidence to conclude that the vans underperform the manufacturer's MPG rating

560

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