The owner of the factory that sells a particular bottled fruit juice claimed 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 s is 5 ml. Use α = 0.03. Will
you reject or not to reject the claim.
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value for two-tailed, degrees of freedom, is and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean
is different than 250, at the significance level.
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