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# (Round all intermediate calculations to at least 4 decimal places.) A machine that is programmed to package 1.20 pounds of cereal in each cereal box...

**(Round all intermediate calculations to at least 4 decimal places.)**

A machine that is programmed to package 1.20 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. Use __Table 2__.

**a.**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.

a.) H0: µ ≥ 1.20; HA: µ < 1.20

b.) H0: µ ≤ 1.20; HA: µ > 1.20

c.) H0: µ = 1.20; HA: µ ≠ 1.20

**b.**Calculate the value of the test statistic. **(Round your answer to 2 decimal places.)**

Test statistic ___________

**c-1.**Approximate the p-value.

a.) p-value < 0.01

b.) 0.01 ≤ p-value < 0.025

c.) 0.025 ≤ p-value < 0.05

d) 0.05 ≤ p-value < 0.10

e.) p-value ≥ 0.10

**c-2.**What is the conclusion at a 5% level of significance?

a.) Reject H0 since the p-value is greater than α.

b.) Reject H0 since the p-value is smaller than α.

c.) Do not reject H0 since the p-value is greater than α.

d.) Do not reject H0 since the p-value is smaller than α.

**d-1.**Calculate the critical value(s) at a 5% level of significance. **(Round your answer to 3 decimal places.)**

Critical value(s) ± _______

**d-2.**Can you conclude that the machine is working improperly? Yes or No ?