Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It is believed that the machine is underfilling the bags. A 19 bag sample had a mean of 412 grams with a variance of 784. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

Answer 1

)H0: = 419

Ha: < 419

Test statistics

t = - / ( S / sqrt(n) )

= 412 - 419 / ( sqrt(784 ) / sqrt(19) )

= -1.09

This is test statistics value.

Critical value at 0.025 level with 18 df = -2.101

Since test statistics value > -2.101, we do not have sufficient evidence to reject H0.

We fail to reject the null hypothesis.

from T table,

With test statistics of -1.09 an df of 18, p-value = 0.1450