A competing automaker claims its midsize cars are normallydistributed with a mean 33 and sigma...

A competing automaker claims its midsize cars are normally distributed with a mean 33 and sigma of 0.7. One car is selected for testing and gets 31.2 mpg. Does this observation contradict the automaker’s claim?

Solutions

Expert Solution

Answer to the question:

To test the hypothesis we will use Z test. Our hypothesis are given as:

At 1% level of significance the critical value of the Z statistic is 2.33. So, if the absolute value of the calculated Z statistic is less than 2.33, then we will not reject the null hypothesis and will conclude that there is no significant difference between the car performance and automaker’s claim.

On the other hand, if the absolute value of the calculated Z statistic is more than 2.33, then we will reject the null hypothesis and will conclude that there is a significant difference between the car performance and automaker’s claim.

Let us proceed to the Z test:

The absolute value of the calculated Z statistic is 2.57 which is greater than the tabulated critical value of the Z statistic (at 1% level of signficance) 2.33, thus, we will reject the null hypothesis and will conclude that there is a significant difference between the car performance and automaker’s claim.

Rahul Sunny answered 2 years ago

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