What are the Hypotheses

In order to meet company (and government) standards, the management of a soft drinks company need to ensure the humidity of their bottling room is maintained between a specific range of temperatures, thus ensuring there is no under or over fill of the bottles. Management periodically request for test to be taken on their bottle filling operations and the latest test produced the result in Table 1. The results are based upon the filling of fifty, two litre bottles with the same soft drink.

The company chairman stated that the average fill should be 2.00 litres. Use a 5% level of significance to test the hypothesis that there is a filling difference from 2.00 litres.

Use the following information to help you solve the problem:

1. What are the hypotheses H₀ and H₁ (or HA)
2. Determine whether the test is one or two tailed. (if the test is one tailed-is it right hand or left hand)
3. Determine the critical values based upon your hypotheses and your significance value
4. Set up and Calculate the test statistic
5. Compare the test statistic to the critical values-what is your decision
6. If instead of a 5% level of signifance, you were to use a 10% (ten percent) level of significance? Explain
7. Suppose the population mean, sample mean and sample standard deviation all remained constant. Determine the minimum number of bottles to sample, at the point of the occurrence of the decision between rejecting and not rejecting the null hypothesis, when using a 5% level of significance.