THIS IS AN EXAMPLE OF LITERALLY WHAT I WANT A SIMILAR WORK, BUT FOLLOW WHAT MY TEACHER IS ASKING FOR:

TABLE 10.8 Test Statistics and pvalues for Hypothesis Tests Hypotheses Test Statistic H0 p1 p2 S 0 z = 0.175 0.10 = 1.7748 0.038 HA p1 -p2 > 0 01429 1 01429 1 1 ' m + m H0 p1 _p2 0 20 0.3125 (1 0.3125) + 0.0833 (1 0.0833) 160 120 When doing your data analysis, please set up and test the following hypotheses: 1. The population mean wage for workers with high school diplomas is greater than the population mean wage for workers who do not have a high school diploma. 2. The population mean wage for workers with high school diplomas is more than $2 higher than the population mean wage for workers who do not have a high school diploma. 3. The population mean wage for workers with high school diplomas is more than $1 higher than the population mean wage for workers who do not have a high school diploma. 4. The population mean wage for workers with a bachelor's degree is greater than the population mean wage for workers with a only high school diploma. 5. The population mean wage for workers with a bachelor's degree is more than $10 higher than the population mean wage for workers with only a high school diploma. 6. The population mean wage for workers with a bachelor's degree is more than $9 higher than the population mean wage for workers with only a high school diploma. For ease of comparison, assume xbar1 is the sample mean wage for workers with a high school diploma; xbar2 is the sample mean wage for workers with no high school diploma; and xbar3 is the sample mean wage for workers with a bachelor's degree. Hint: when testing whether one population mean is bigger that the other, use the bigger mean first in calculating the difference. For example, when testing if mean wage for workers with a bachelor's degree is bigger than the mean wage for high school, use (xbar3 minus xbar1). For each of the hypothesis tests, please note: 1. We cannot assume that the unknown population variances are equal. 2. Implement the tests at the 5% significance level. 3. Please use the p-value approach to test each hypothesis. Please refer to "10.4: Writing with Data" at the end of Chapter 10 and use the table format provided there to show your hypothesis, your test statistic and the corresponding.p-value. Please note the table not only shows the formula, but shows the numbers you plugged into the formula as well as if you are using a t or a z statistic. At least 20 points will be deducted if you do not use this table format to share your test results. 4. Please write about three paragraphs to interpret the data, and to summarize the main findings. Please address your writing to your high school student audience. Your writing should be clearly related to the above table you have created to summarize the results of your hypothesis tests.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 4 13.33% 23 25 24 4 13.33% 26 28 27 12 40.00% 29 31 30 3 10.00% 32 34 33 5 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 30.00% 18 20 19 WNDO 6.67% 21 23 22 10.00% 24 26 25 3.33%100.00% No High School Diploma Frequency Distribution Number of 6 Mean 1256 Classes Range 137 Standard M Deviation Class Width 3 95% Condence 11.5366, 13.5834 Interval Class Midpoint Frequency Relative Lower Limit Upper Limit Frequency 4 6 5 1 3.3 3% 7 9 8 2 6.67% 10 12 11 10 33.33% 13 15 14 12 40.00% 16 18 17 4 13.33% 1 9 2 1 20 1 3.3 3% 30 l 00.00% Guide and Important Points in the presentation of results. lst paragraph It must be mentioned here that the wage of bachelor's degree holders are significantly larger than those high school diploma holders and no high school diploma. You must mention the numerical values of the means for each group here. You could mention here that the wage of baohelor-s degree could be 2 times the other two groups. You then could say to the students that it is truly an advantage if you have the proper education as the wage increases every time you earn a level of education. It is very important to emphasize that nishing high school and continuing to a bachelor's degree will give a larger wage. 2nd Paragraph You could focus on the frequency distribution here and the bar graphs. The bar graph for the bachelors degree wage distribution shows a symmetrical curve which means that the values are concentrated at the center of the distribution. This will tell you that the mean could be a good representation of the wage. The bar graph of the high school diploma wage distribution shows that more of the data points are to the le of the distribution. This means that there are more data points on the lower side of the wage distribution. The bar graph of the no high school diploma wage distribution shows that more of the data points are also to the le of the distribution. This means that there are more data points in the lower side of the wage distribution. 3rd paragraph You could focus on the condence intervals here. It is mentioned that you have tackled a proper reporting on the condence interval in your class. You should be using those points to make a convincing discussion of the condence interval presented. As a nal sentence, mention that it is truly an advantage to continue education at least up to bachelor's degree to get high wage rates. Graphs: Bachelor's Degree Wage Distribution 40.00% 30.00% 20.00% Relative Frequency 10 00% 0.00% 30 Wage HighSchool Diploma Wage Distribution 30.00% 20.00% 10.00% >t u c at is E .3 E u n: \fMany 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 han 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 15