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 0.16 pound, respectively.(You may find it useful to reference the appropriate table:ztableorttable)

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: 3.00;H_A:< 3.00

b)H₀: 3.00;H_A:> 3.00

c)H₀:= 3.00;H_A: 3.00

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

Test Statistic=

b-2.Find thep-value.

a)0.05 p-value < 0.10

b)0.02 p-value < 0.05

c)0.01 p-value < 0.02

d)p-value 0.10

e)p-value < 0.01

c-1.What is the conclusion at the5% significance level?

multiple choice 3

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 4

a)Yes

b)No