Can someone explain how we come to this? ( x = 573.125 and s =19.809) in the answer to this question below?

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how to test at the 10% level of significance if the detergent production meets the company specifications and is operating correctly.

Answer:

a) Tmean lifetime of batteries has now been reduced in relation to previous years.

b) detergent production does not meets the company specifications and is not operating correctly.

Explanation:

a) we need to tests the hypothesis

Ho: 

 -3.70

0.05

-3.70 < mean lifetime of batteries has now been reduced in relation to previous years.

b) we need to test the hypothesis

Ho: 

<

x = 573.125 and s =19.809

the test statistics is given by

t=

19.809/sqrt(8))

= -3.837

at n-1 degrees freedom, the critical value t0.1 = -1.415

since -3.837 < -1.415, reject Ho and conclude that  detergent production does not meets the company specifications and is not operating correctly.