A soda manufacturer is interested in determining whether it's bottling machine tends to overfill. Each bottle is supposed to contain 15 ounces of fluid. A random sample of 30 bottles was taken and found that the mean amount of soda of the sample of bottles is 13.4 ounces with a standard deviation of 2.98 ounces. if the manufacturer decides on a significance level od 0.05 test, should the null hypothesis be rejected?
The following null and alternative hypotheses need to be tested:
This corresponds to a right-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 right-tailed test is
The rejection region for this right-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for right-tailed, degrees of freedom, is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean is greater than 15, at the significance level.
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