A bakery stated that the average number of breads sold daily is 3000. An employee thinks that the actual
value might differ from this and wants to test this statement. The correct hypotheses are: (I think it is 1)
(1) H0 : ¦Ì = 3000 H1 : ¦Ì not= 3000
(2) H0 : ¦Ì > 3000 H1 : ¦Ì ¡Ü 3000
(3) H0 : ¦Ì not= 3000 H1 : ¦Ì = 3000
(4) H0 : ¦Ì > 3000 H1 : ¦Ì not= 3000
(5) H0 : ¦Ì ¡Ü 3000 H1 : ¦Ì > 3000
The correct hypotheses in this case are:
(1) H0 : µ = 3000, H1 : µ ≠ 3000
H0 (null hypothesis) represents the assumption that the average number of breads sold daily is 3000. H1 (alternative hypothesis) suggests that the actual value might differ from 3000, indicating that it could be either less or greater than that.
The other answer options do not accurately represent the intended hypotheses. Let me explain why:
(2) H0 : µ > 3000, H1 : µ ≤ 3000
This hypothesis suggests that the average number of breads sold daily is greater than 3000, which is not the employee's concern. The alternative hypothesis states that it might be less than or equal to 3000, which is not consistent with the employee's claim.
(3) H0 : µ ≠ 3000, H1 : µ = 3000
This hypothesis suggests the reverse of the desired explanation. It assumes the average number of breads sold daily is different from 3000 as the null hypothesis, and the alternative hypothesis assumes it to be exactly 3000.
(4) H0 : µ > 3000, H1 : µ ≠ 3000
Similarly to option (2), this hypothesis assumes the average number of breads sold daily to be greater than 3000 as the null hypothesis, which is not what the employee is concerned with. The alternative hypothesis states that it might be different from 3000, which aligns with the employee's claim.
(5) H0 : µ ≤ 3000, H1 : µ > 3000
This hypothesis assumes the average number of breads sold daily to be less than or equal to 3000 as the null hypothesis, but the alternative hypothesis states that it might be greater than 3000. This is not consistent with the employee's concern.
Therefore, the correct choice is (1) H0 : µ = 3000, H1 : µ ≠ 3000.