Final answer:
To determine the highest confidence level at which the null hypothesis would be accepted, calculate the margin of error and compare it to the sample mean difference. If the margin of error is less than or equal to the sample mean difference, accept the null hypothesis at that confidence level. If the margin of error is greater than the sample mean difference, reject the null hypothesis. In this case, the null hypothesis would be accepted at a 95% confidence level.
Step-by-step explanation:
To determine the highest confidence level at which the null hypothesis would be accepted, we need to calculate the margin of error and then compare it to the sample mean difference.
The margin of error can be calculated by multiplying the standard deviation of the distribution of the difference in sample means by the critical value corresponding to the desired confidence level. Since the sample mean difference is 8.5 liters and the standard deviation is 4.5 liters, the margin of error is: 4.5 * Z = 8.5, where Z is the critical value.
We can use a table or calculator to find the critical value that corresponds to the desired confidence level. If the margin of error is less than or equal to the sample mean difference, we accept the null hypothesis at that confidence level. If the margin of error is greater than the sample mean difference, we reject the null hypothesis.
In this case, Z for a 95% confidence level is approximately 1.96. Therefore, the margin of error is 4.5 * 1.96 = 8.82 liters. Since the margin of error is greater than the sample mean difference of 8.5 liters, the null hypothesis would be accepted at a 95% confidence level.