Question

In auto racing, a pit crew claims that its mean pit stop time (for 4 new tires and fuel) is less than 13 seconds. A random selection of 32 pit stop times has a sample mean of 12.9 seconds and a standard deviation of 0.19 second. Is there enough evidence to support the claim at α = 0.01?

Answer 1

Solution :

let X be a pit stop time of auto race.

here we have given that:

sample size (n)=32

sample mean () = 12.9

And Known standard deviation is () = 0.19

level of significance () = 0.01

is population mean.

Here we have known sample standard deviation for testing we used Z-test.and find the evidence.

Hypothesis :

H0 :

Ha :

Test Statistics :

put all the information in Z statistic,

Z = 2.98

Now critical Z - Value ,

Z- critical :

  

at ( = 0.01 )

(from standad normal table)

Criteria :

If the We may reject the H0 at % level of significance.

Here also 2.98 > 2.33 ,So we may say that reject H0 at 1% level of significance .

Conclusion :

Accept Ha :

The claim of pit crew that mean pit stop time is less than 13 second is may correct.

there is enough event to support the claim.

For value of we saw the below standaed normal statistical table 2.3 horizontally and 0.03 vertically there is value 0.0099 is appoximate to 0.01.