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 the standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. (You may find it useful to reference the appropriate table: z table or t table)

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.

• H₀: 1.20; H_A: < 1.20
• H₀: 1.20; H_A: > 1.20
• H₀: = 1.20; H_A: 1.20

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. Find the p-value.

• p-value 0.01
• 0.01 < p-value 0.02
• 0.02 < p-value 0.05
• 0.05 < p-value 0.10
• p-value > 0.10

c-1. What is the conclusion at a 5% significance level?

• Reject H₀ since the p-value is greater than significance level.
• Reject H₀ since the p-value is smaller than significance level.
• Do not reject H₀ since the p-value is greater than significance level.
• Do not reject H₀ since the p-value is smaller than significance level.

c-2. Can you conclude that the machine is working improperly?

• Yes
• No