For each of the following pairs of hypotheses determine whe

\" For each of the following pairs of hypotheses,
determine whether each pair represents valid hypotheses for a hypothesis test. Explain reasons for any pair that is indicated to be invalid.

a. H0:m = 15,HA:m > 15

b. H0:m = 20,HA:m =? 20

c. H0:m < 30,HA:m> 30

Solution

a. H0:m = 15,HA:m > 15

INVALID. The null hypothesis must be the opposite of Ha, so it must have used <=.

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b. H0:m = 20,HA:m = 20 [VALID]

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c. H0:m < 30,HA:m> 30

INVALID. The Ho must always have an equality, so it must have been <=.

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d. H0:m <= 40,HA:m >= 40

INVALID. Only the null hypothesis must have the equality. Thus, Ha must have used >.

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f. H0:m <= 50,HA:m > 55 [VALID]