Final answer:
An 80% confidence interval provides an estimate of a range where the true population parameter is likely to be found. The significance of the difference between two means is assessed by whether this interval includes zero, which would indicate no significant difference at the 80% confidence level. To determine the right answer from the options, one must perform the correct calculations using the data given for the samples.
Step-by-step explanation:
The confidence interval provides an estimated range of values which is likely to include the true unknown parameter of the population, such as the difference in mean weekly earnings in a given case. The fact that the interval includes zero or not determines if there is a statistically significant difference between the two means. To construct an 80% confidence interval for the difference between two means, we use the formula for the confidence interval of the difference between two independent means (with known standard deviations), taking into account the sample sizes, means, and standard deviations of the two samples.
To make an inference about the significance of the difference in pay between the two groups of workers, we would compare the resulting confidence interval to zero. If the interval includes zero, we would not consider the difference to be significant at the 80% confidence level. Note that the options provided (a-d) must be calculated based on the data given for the two samples of workers. We will use statistical software or perform a manual calculation to find the correct interval, as the intervals listed in the question options do not directly apply without further calculation.