Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 414

gram setting. It is believed that the machine is underfilling the bags. A 16 bag sample had a mean of 405 grams with a variance of 625. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answer 1

x̅ = 405, s² = 625, n = 16

Null and Alternative hypothesis:

Ho : µ = 414 ; H1 : µ < 414

Test statistic:

t = (x̅- µ)/(√(s²/n) = (405 - 414)/√(625/16) = -1.44

df = n-1 = 15

Critical value :

Left tailed critical value, t-crit = T.INV(0.025, 15) = -2.131

Reject Ho if t < -2.131

Or using p-value :

p-value = T.DIST(-1.44, 15, 1) = 0.0852

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to support the claim that the bags are underfilled at 0.025 significance level.