Question

A machine that is programmed to package 1.90 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 26 cereal boxes, the mean and the standard deviation are calculated as 2.02 pounds and 0.24 pound, respectively. (You may find it useful to reference the appropriate table: z table or 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, HON 21.90; HAN < 1.90 HON $ 1.90; HAIN > 1.90 OH: N - 1.90; HA: N * 1.90 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.) Test statistic

Answer 1

Solution:

n = 26 ,

x̄ = 2.02 , s = 0.24

a.

Claim : If the machine is working properly, that is it is either underfiting or overfiting.

• H0 : µ = 1.90; µ ≠ 1.90

b.

test statistic = (x̄-µ)/(s/√n)

= (2.02-1.90)/(0.24/√26)

= 2.5495

Test Statistic = 2.5495