Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 448 gram setting. It is believed that the machine is underfilling the bags. A 51 bag sample had a mean of 443 grams with a variance of 225. Assume the population is normally distributed. A level of significance of 0.02 will be used. Specify the type of hypothesis test.

Answer 1

H0: = 448

Ha: < 448

Test statistics

t = ( - ) / Sqrt ( S² / n)

= ( 443 - 448) / sqrt ( 225 / 51)

= -2.38

df = n - 1 = 51 - 1 = 50

From T table,

Critical value at 0.02 significance level with 50 df = -2.108

Since test statistics < -2.108 , Reject H0.

We conclude at 0.02 level that we have sufficient evidence to conclude that the machine is underfilling the bags.