Question

The owner of a factory that sells a particular bottled fruit juice claims the the average capacity of their product is 250 ml to the test claim a consumer group gets a sample of 100 such bottles calculates the capacity of each bottle and then finds the mean capacity to the be 248ml.The standard deviation is 5ml significance level is 0.5 is the claim true

Answer 1

Given that:

$\mu =250$

$\:\overline{x}=248$

$\:\:n=100$

$\alpha =0.5$

$\:\:s=5$

(a). There is enough sample size to apply central limit, because here $n=100>30$

(b). Hypothesis: $H_o:\mu=250$

$H_1:\mu\:\not=$ $250$

(c). This is a two tailed test

(d). The test statistic is: $t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}$

$t=\frac{248-250}{\frac{5}{\sqrt{100}}}$

$t=-4$

$\left|t\right|=4$

From the critical $t-value$ table, $t_c$ at $\alpha=0.5$ with $df=n-1=99$

is $t_c=$ $0.68$

Here $\left|t\right|=4>t_c=0.68$

Therefore, we reject the $H_o$ at $50$% level of significance and the claim is not true.

Hence, we conclude that there is no sufficient evidence to conclude that the average capacity of the product is $250ml$ .