Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 406 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 401 grams with a standard deviation of 25. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal, State the null and alternative hypotheses. T Tables

Answer 1

Let the weight of the chocolate chips bag be denoted by a random variable X.

Let the population mean $\mu$ be the average weight of the chocolate chip bag.

We test the following Hypothesis,

Null hypothesis, H₀: The bag filling machine works correctly. i.e.
H = 406
v/s

Alternate hypothesis, H₁: The bag filling machine is under filling the bags. i.e.
山<406

We perform the 1 sample t test.

The test statistic T is given by,

Vn(X-) T S

where n = sample size = 26

sample mean =

X = 401

sample standard deviation = s = 25

Therefore,

T = /26(401 – 406) 25

=-1.02

The critical value for is given by

g= 0,05

tan-1 = t0.05,26–1 = 10.05,25 = 1.708

Since

T>-tan-1

We fail to reject the null hypothesis at level of significance.

g= 0,05

That is, the machine is not underfilling the bags.

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