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

A machine that is programmed to package 2.55 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 25 cereal boxes, the mean and standard deviation are calculated as 2.58 pounds and 0.10 pound, respectively. UseTable 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.

H₀: 2.55;H_A:< 2.55H₀: 2.55;H_A:> 2.55H₀:= 2.55;H_A: 2.55

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

Test statistic

c-1.Approximate thep-value.0.10<p-value < 0.200.01 <p-value < 0.020.02 <p-value < 0.05p-value < 0.01p-value0.2

c-2.What is the conclusionat the 5% significance level?RejectH₀since thep-value is greater than.RejectH₀since thep-value is smaller than.Do not rejectH₀since thep-value is greater than.Do not rejectH₀since thep-value is smaller than.

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

Critical value(s)