Question

A machine that is programmed to package 2.35 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 34 cereal boxes, the mean and the standard deviation are calculated as 2.38 pounds and 0.19 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: µ ≥ 2.35; H_A: µ < 2.35

• H₀: µ ≤ 2.35; H_A: µ > 2.35

• H₀: µ = 2.35; H_A: µ ≠ 2.35

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.

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

• p-value < 0.01

c-1. What is the conclusion at the 1% 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

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses: Option C is correct.

b - 1) Test statistic = 0.92

b - 2) p - value > 0.10

c - 1)  Do not reject H₀ since the p-value is greater than significance level.

c - 2) No