The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test.<p>He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis?
To determine the decision regarding the hypothesis, we need to compare the test statistic to the critical value and determine if it falls in the rejection region or non-rejection region.
The given test statistic is 2.21, but we need to find the critical value for a significance level of 0.05. Since the test is a two-sample z test, it follows a standard normal distribution.
To find the critical value, we look up the z-value for a 0.05 significance level in the standard normal distribution table. A significance level of 0.05 corresponds to a two-tailed test, so we divide the significance level by 2 to find the critical value associated with each tail.
For a significance level of 0.025 (0.05 divided by 2), the critical value is approximately 1.96.
Now, we compare the test statistic of 2.21 to the critical value of 1.96.
If the test statistic is greater than the critical value (2.21 > 1.96), it falls in the rejection region. This means we reject the null hypothesis.
If the test statistic is less than or equal to the critical value (2.21 ≤ 1.96), it falls in the non-rejection region. This means we fail to reject the null hypothesis.
In this case, the test statistic of 2.21 is greater than the critical value of 1.96. Therefore, it falls in the rejection region. Thus, we reject the null hypothesis that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine.
In conclusion, the decision regarding the hypothesis is to reject the claim that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine.