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, s^{2} = 625, n = 16

Null and Alternative hypothesis:

Ho : µ = 414 ; H1 : µ < 414

Test statistic:

t = (x̅- µ)/(√(s^{2}/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.

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