Question

A machine that is programmed to package μo (shown on right) pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes.

µo =	1.2

a	Ho: µx = µo         Ha: µx ≠ µo
b	Ho: µx < µo         Ha: µx > µo
c	Ho: µx > µo         Ha: µx < µo
d	Ho: µx ≠ µo         Ha: µx = µo
e	None

Answer 1

Solution:

Given , µ_o  = 1.2

Claim: if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes.

i.e. = or not

So the null and the alternative hypotheses can be written as

Ho: µ_x = µ_o         Ha: µ_x ≠ µ_o            

Option a is correct.

{ Valid signs in H0 are = , and

Valid signs in Ha are , < and >

}