Solution to The owner of a factory that sells a particular bottled fruit juice claims that the … - Sikademy
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Peace Awoke

The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of each bottle, and then finds the mean capacity to be 248 ml. The standard deviation is 5 ml. Is the claim true?

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Here's the Solution to this Question

Here,

\overline{x}=248

n=100

\alpha =0.5

\:s=5

Hypothesis tested are,

H_o:\mu=250

vs

H_1:\mu\:\not= 250

The test statistic is,

t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}=\frac{248-250}{\frac{5}{\sqrt{100}}}={-2\over{1\over2}}=-2\times2=-4.

Therefore,

t=-4

and

\left|t\right|=4

The critical table value, t_{{\alpha\over2},n-1} with \alpha=0.05 with df=n-1=99 is t_{0.025,99}= 1.984217.

The null hypothesis is rejected if |t|\gt t_{0.025,99}

Here \left|t\right|=4>t_{0.025,99}=1.984217

Therefore, we reject the null hypothesis at 5\%% level of significance and conclude that there is no sufficient evidence to show that the average capacity of the product is 250 ml.


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