The average life expectancy of tires produced by the whitney tire company has been 40,000 miles. management believes that due to a new production process, the life expectancy of its tires has increased. in order to test the validity of this belief, the correct set of hypotheses is
a. h_0: mu < 40,000 h_a: mu greaterthanorequalto 40,000
b. h_0: mu lessthanorequalto 40,000 h_a: mu > 40,000
c. h_0: mu > 40,000 h_a: mu lessthanorequalto 40,000
d. h_0: mu greaterthanorequalto 40,000 h_a: mu < 40,000

b. Null hypothesis :

Alternative hypothesis:

Explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the Management try to proof that due to a new production process, the life expectancy of its tires has increased. So this needs to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.

Null hypothesis :

Alternative hypothesis:

Other important thing is that on the alternative hypothesis we never can have the symbol equal.

Based on this the best option on this case is b.

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could you go a bit more in depth with you question? it's quite hard to understand. as soon as you do that i will be glad to : )