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?
A. Reject the null hypothesis; there is a significant difference.
B. This is a two tail test and the critical value for the test is 1.96.
C. There is not enough data available to answer the question.
D. Accept the null hypothesis; there is not a significant difference
To make a decision regarding the hypothesis, we need to compare the test statistic to the critical value.
Since the test was conducted at a 0.05 significance level, we need to compare the test statistic of 2.21 with the critical value associated with the level of significance.
For a one-tailed test with a 0.05 significance level, the critical value is approximately 1.645. Since the test statistic of 2.21 is greater than the critical value of 1.645, we can reject the null hypothesis.
Therefore, the correct decision regarding the hypothesis is:
A. Reject the null hypothesis; there is a significant difference.
To make a decision regarding the hypothesis, we need to compare the test statistic to the critical value. In this case, the owner conducted a two-sample z-test to compare the mean weights of the bottles filled by two different machines, Orno and Edne.
The claim being tested is 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.
The decision regarding the hypothesis is determined by comparing the test statistic to the critical value at the chosen significant level (0.05 in this case).
If the test statistic falls in the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis.
Given that the test statistic is 2.21, we need to determine if it falls in the rejection region (or critical region) at the 0.05 significant level.
Since this is a one-tailed test (claiming that the mean weight of the Orno machine is greater), we need to compare the test statistic to the critical value for a one-tailed test at the chosen significant level.
The critical value for a one-tailed test at the 0.05 significant level is 1.645 (for a lower tail test) or 1.645 (for an upper tail test).
Because the test statistic of 2.21 is greater than the critical value of 1.645, it falls in the rejection region. Therefore, we reject the null hypothesis.
So, the correct answer is A. Reject the null hypothesis; there is a significant difference.