Solve the problem. Use the critical-value approach.
A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid ounces. A random sample of 20 filled bottles produced the following volumes in fluid ounces:
These data are summarized on the following histogram:
Using technology, perform the following hypothesis test: at the 5% significance level, determine whether the fill volume is less than the supposed value. Comment on the appropriateness of the test.
◦ Test statistic: t = -1.8063; Critical value: -2.0921.
Since the test statistic is greater than the critical value, do not reject the null hypothesis
There is insufficient evidence to conclude that the fill volume is below 16.2 oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
◦ Test statistic: t = -1.8063; Critical value: -2.0921.
Since the test statistic is greater than the critical value, do not reject the null hypothesis
There is insufficient evidence to conclude that the fill volume is below 16.2 oz. The conclusion is on sound statistical ground.
◦ Test statistic: t = -1.8063; Critical value: -1.729.
Since the test statistic is less than the critical value, reject the null hypothesis H
0: μ = 16.2 oz.
There is sufficient evidence to conclude that the fill volume is below 16.2 oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
◦ Test statistic: t = -1.8063; Critical value: -1.7254.
Since the test statistic is less than the critical value, do not reject the null hypothesis H
0: μ = 16.2 oz.
There is insufficient evidence to conclude that the fill volume is below 16.2 oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
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