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 42 cereal boxes, the mean and the standard deviation are calculated as 1.26 pounds and 0.15 pound, respectively.(You may find it useful to reference the appropriate table:z tableort 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. (multiple choice)

a. H₀: 1.20;H_A:< 1.20

b. H₀: 1.20;H_A:> 1.20

c. 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 thep-value. (multiple choice)

a. p-value < 0.01

b. p-value0.10

c. 0.05p-value < 0.10

d. 0.01p-value < 0.02

e. 0.02p-value < 0.05

c-1.What is the conclusion at the1% significance level? (multiple choice)

a. RejectH₀since thep-value is greater than significance level.

b. RejectH₀since thep-value is smaller than significance level.

c. Do not rejectH₀since thep-value is greater than significance level.

d. Do not rejectH₀since thep-value is smaller than significance level.

c-2.Can you conclude that the machine is working improperly? (multiple choice)

a. Yes

b. No