Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 412 gram setting. It is believed that the machine is underfilling the bags. A 8 bag sample had a mean of 404 grams with a standard deviation of 26 26 . 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

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: the bags are not under filled.

Alternative hypothesis: H_a: the bags are under filled.

H₀: µ = 412 versus H_a: µ < 412

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 412

Xbar = 404          

S = 26

n = 8

df = n – 1 = 7

α = 0.025

Critical value = -2.3646

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (404 - 412)/[26/sqrt(8)]

t = -0.8703

P-value = 0.2065

(by using t-table)

P-value > α = 0.025

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the bags are under filled.