Suppose you believe that, in general,graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs. Describe a statistical experiment that could help test your belief.
The first thing you need is a random selection of graduates whose salaries can be compared... and that's probably the trickiest bit, because getting a genuinely random selection of graduates could more difficult than you might think. Suppose for example your subject is accountancy, and you want to compare salaries of graduate accountants with those of graduate chemists. Where can you find a lot of accountants? In an accountancy firm, of course - but you won't find many chemists there. So you look up an accountancy firm and a chemical company in the phone book, and start asking people at random what their salaries are... and you'll get absolutely nowhere, because they probably won't tell you! Also if your companies are in different cities, you could find that the cost of living is higher in one city than the other - and that could be reflected in the salaries. On top of that, you could find for example that the average ages of the two groups are different - in which case the older group is probably paid more than the younger group, quite simply because they've been working longer, and their careers are more advanced.
You'll need to control as many extraneous factors like these as you can when selecting your groups, so I'd suggest that you look at all the graduates from a set of specific classes (i.e. they graduated from the same schools/colleges/universities or whatever at the same time), and then went to work in the same areas (or at least comparable areas in terms of the cost of living, cost off housing, local tax rates etc). Now you need to start thinking about HOW you're going to get them to tell you what their salaries are - and making sure that you compare like with like there as far as possible there as well. Is it possible for example that highly-paid accountants are going to be more cagy about telling you what they earn than poorly-paid chemists? I don't have an answer to that one, but it might help you start thinking about what you'll need to consider when setting up your experiment.
Thanks for the response
To test your belief that graduates who have majored in your subject are offered higher salaries upon graduating than graduates of other programs, you can conduct a statistical experiment. Here's a step-by-step description of the experiment:
1. Define the population: Identify the population of interest, which in this case is all graduates who have majored in your subject and graduates from other programs.
2. Sample selection: Randomly select a sample of graduates from your subject's major and an equal-sized random sample of graduates from other programs. Ensure that the samples are representative of the entire population.
3. Data collection: Collect data on the starting salaries of the graduates in each group. This can be done through surveys, interviews, or existing data sources.
4. Hypotheses formulation: Formulate the null hypothesis (H0) and alternative hypothesis (Ha). In this case, the null hypothesis could be that there is no difference in salaries between the two groups, and the alternative hypothesis could be that graduates from your subject's major are offered higher salaries.
5. Statistical test selection: Choose an appropriate statistical test to analyze the data. Depending on the characteristics of your data (e.g., sample size and data distribution), you can use a t-test, ANOVA, or a non-parametric test like the Mann-Whitney U test.
6. Perform statistical analysis: Apply the chosen statistical test to the data, comparing the salaries of the two groups. Calculate the test statistic and obtain the p-value.
7. Interpret the results: Based on the p-value obtained, determine if there is sufficient evidence to reject the null hypothesis. If the p-value is below a predetermined significance level (e.g., 0.05), it suggests that there is a significant difference in salaries between the two groups.
8. Draw conclusions: Based on the results, draw conclusions about whether there is evidence to support your belief that graduates who have majored in your subject are offered higher salaries compared to graduates from other programs.
Note: It is important to consider other factors that could influence salary differences, such as the prestige of the institution, work experience, or geographical location, to ensure the validity of your conclusions.
To test the belief that graduates who have majored in your subject are offered higher salaries upon graduating than graduates of other programs, you can design a statistical experiment. Here's a step-by-step approach to conducting this experiment:
1. Define the variables: Determine the independent variable, which in this case is the major, and the dependent variable, which is the salary offered.
2. Sample selection: Randomly select a representative sample of graduates from your subject's major and graduates from other programs. Ensure the sample sizes are large enough for valid statistical analysis.
3. Data collection: Collect relevant data on the salaries offered to the graduates. You can obtain this data through surveys, online sources, official salary reports, or by contacting the graduates directly.
4. Data analysis: Compare the average salaries offered to graduates from your subject's major with the average salaries offered to graduates from other programs. You can use descriptive statistics, such as means and medians, to summarize the data and identify any differences.
5. Hypothesis testing: Formulate a null hypothesis (H0) assuming that there is no significant difference in salaries offered between your subject's major and other programs' graduates. The alternative hypothesis (Ha) would then state that there is a significant difference.
6. Statistical test selection: Choose an appropriate statistical test to compare the means of the two groups. Depending on the nature of the data and the sample sizes, you can consider using a t-test, such as an independent samples t-test or a one-way ANOVA.
7. Perform the statistical test: Calculate the test statistic and the corresponding p-value. The p-value will help determine the statistical significance of the difference in salaries between the two groups. Generally, a p-value less than 0.05 is considered statistically significant.
8. Interpret the results: If the p-value is less than the defined significance level (e.g., 0.05), you can reject the null hypothesis and conclude that there is evidence to support your belief. Conversely, if the p-value is not significant, you would fail to reject the null hypothesis, indicating that there is no significant difference in salaries offered.
9. Draw conclusions: Based on the results, you can make informed conclusions about whether graduates who major in your subject tend to receive higher salaries upon graduating compared to graduates of other programs.
Remember, conducting a statistical experiment is essential to test the belief accurately. It ensures that the results are not biased and provides a valid statistical inference.