A 95% confidence level for the difference between u1 and u2 runs from -2 to +6. From this we can infer that
a. u1 is probably greater than u2.
b. u1 is probably less than u2.
c. there may be no difference at all between u1 and u2.
d. the difference between u1 and u2 is not very large in any case.
To infer the meaning from the 95% confidence interval for the difference between u1 and u2, we need to understand what a confidence interval represents.
A confidence interval is a range of values around an estimate that is likely to contain the true value of the parameter being estimated. In this case, the parameter being estimated is the difference between u1 and u2.
Given that the 95% confidence interval is from -2 to +6, we can conclude that we are 95% confident that the true difference between u1 and u2 falls within this range.
Since the confidence interval includes both positive and negative values (from -2 to +6), we can infer that there may be no significant difference (i.e., no statistically significant evidence) between u1 and u2. This means that option c. "there may be no difference at all between u1 and u2" is the correct inference to make from the given information.
It is important to note that a confidence interval does not provide conclusive proof, but rather a measure of uncertainty about the estimated parameter.