1 2 3 4 A drink vending machine is adjusted so that on avera

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A drink vending machine is adjusted so that, on average, it is expected to dispense 220 ml of fruit juice (with a standard deviation of 10 ml) into a plastic cup. However, the machine has a tendency to become misaligned and the owners believe it may be putting out too much juice. A sample of 45 drinks is taken to test the adjustment of the machine, and results show that on average it actually dispensed 223 ml.

Solution

1.

The claim (Ho) is that it is putting too much juice.

Thus,

Ho: u >= 220 [option c]

[Normally, it is Ha that is the claim. Thus, I would have answered Ho: u<=220 if not because of your choices. You can bring this up to your professor.]

2.

Using a table, the critical value for a right tailed 0.05 test is

z = +1.65 [ONLY +, OPTION C]

3.

Here,

z = (X - u) * sqrt(n) / s

= (223 -220)*sqrt(45) / 10

= 2.01246118 = 2.01 [OPTION B]

Thus, we FAIL TO REJECT THE NULL HYPOTHESIS, according to how we formulated the hypothesis above.

[It seems that your class has a different convention on this one, as Ho: u<= 220 was not in the choices of part 1. So, I chose that option, and that option influenced this answer. If the italicized text in #1 is correct, it should have been REJECT THE NULL HYPOTHESIS.]

4.

As the machine is shown to put out too much juice, then:

OPTION C: They should adjust the machine so that the machines put out less juice.