Follow these steps:

Many people had trouble explaining why they were creating confidence intervals and how to interpret these confidence intervals and use them to make their case to their audience. Although the average wage for each level of education is different, you have to ask yourself what is the added information that making the confidence intervals gives you beyond just the mean wage that we calculated for each of the categories. For example, you can say to the students: "As you can see, the mean wage for workers with a bachelor's degree is $27.55 versus $14.72 for workers with a high school diploma and only $12.25 for workers with no high school diploma. But we just calculated each of these by taking a sample of only 30 workers. Maybe, there was something peculiar about the samples we did take; maybe these averages do not accurately reflect what the true average wage for each of these categories really is in the larger workforce? In order to get more clarity on these estimates, we are going to use confidence intervals. Table gives you 95% confidence intervals for each of the three categories of education. As you can see, the confidence interval for the mean wage for a bachelor's degree is $25.95 to $29.14. Here is the interpretation: we can claim that this particular confidence interval that we created using this particular sample mean has a 95% chance of capturing the (fixed but unknown) true population mean; it is telling us something about what our population mean might be, but we are not 100% sure; we are only 95% sure. Another way to say this is that, based on our sample of mean, we are 95% confident that the true average wage for workers with a bachelor's degree in the population is somewhere between $25.95 and $29.14. Similarly, we can claim with 95% confidence that the true population average wage for workers with only a high school diploma is somewhere between $13.12 and $16.31. Furthermore, the upper limit of the confidence interval ($16.31) for high school diploma is considerably lower than the lower limit for the confidence interval for a bachelor's degree ($25.95), meaning there is no overlap of the two confidence intervals. The fact that there is no overlap allows us to claim that the mean average wage for a bachelor's degree is probably higher than for workers with only a high school diploma. By contrast, when we compare the upper limit of the confidence interval for no high school with those with a high school diploma, the upper limit for no high school ($13.62) is higher than the lower limit for those with a high school diploma ($13.12). For example, the true population mean could be $13.50, which is included in both confidence intervals. As a result, we cannot claim that the population true average is higher for workers with a high school diploma versus no high school diploma. The real returns to education seem to be with a bachelor's degree. Frequency tables: . Bins have to be of equal size for a given frequency table. Otherwise the frequency table loses its meaning. They should be easy to read also. And I asked you to not create more than 10 bins. Please check the textbook's advice about creating bins for frequency tables. Here is one example of what you could have done for the bachelor's data: Wage Range Frequency Rel. Frequency 15t u c at is E .3 E u n: Case Study 2: Returns to Education Bachelor's Degree Frequency Distribution Number of 6 Mean 27.55 Classes Range 16.4 Standard 4.27 Deviation Class Width 3 95% Confidence 26.022, 29.078 Interval Class Midpoint Frequency Relative Lower Limit Upper Limit Frequency 20 22 21 13.33% 23 25 24 4 13.33% 26 28 27 12 40.00% 29 31 30 10.00% 32 34 33 16.67% 35 37 36 2 6.67% 30 100.00% High School Diploma Frequency Distribution Number of 6 Mean 14.72 Classes Range 18.2 Standard 4.26 Deviation Class Width 4 95% Confidence 13.1956, 16.2444 Interval Class Midpoint Frequency Relative Lower Limit Upper Limit Frequency 8 11 9.5 7 23.33% 12 14 13 26.67% 15 17 16 9 30.00% 18 20 19 6.67% W NI 21 23 22 10.00% 24 26 25 1 3.33%