A machine that is programmed to package 3.00 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 46 cereal boxes, the mean and the standard deviation are calculated as 3.03 pounds and 0.08 pound, respectively.(You may find it useful to reference thettable.) 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. multiple choice 1

• H₀: 3.00;H_A:< 3.00
• H₀: 3.00;H_A:> 3.00
• H₀:= 3.00;H_A: 3.00

b-1.Calculate the value of the test statistic.(Round final answer to 2 decimal places.) b-2.Find thep-value. multiple choice 2

• p-value < 0.01
• p-value0.10
• 0.05p-value < 0.10
• 0.01p-value < 0.02
• 0.02p-value < 0.05

c-1.What is the conclusion at the10% significance level? multiple choice 3

• Do not rejectH₀since thep-value is smaller than significance level.
• Do not rejectH₀since thep-value is greater than significance level.
• RejectH₀since thep-value is smaller than significance level.
• RejectH₀since thep-value is greater than significance level.

c-2.Can you conclude that the machine is not working properly? multiple choice 4

• No
• Yes