Objective: In this practical exercise, you are required to select a topic within your major discipline or an area of personal interest. Collect data related to hypothesis testing and confidence intervals for either one or two populations. Apply hypothesis testing and confidence intervals, interpret the results, and draw appropriate conclusions. Refrain from using data provided in lecture slides.
Assignment Guidelines:
- Topic Selection:
- Choose a topic within your major discipline or a personal area of interest.
- Collect data relevant to hypothesis testing and confidence intervals for one or two populations.
- Data can be obtained online or from other sources.
- Individual or Group Work:
- Decide whether you want to work individually or collaborate with a group (maximum of 3 students).
- If in a group, include the names of all group members on any submitted work.
- Clearly Stated Objectives:
- Clearly state the objectives of your research.
- Define specific questions or hypotheses that your study aims to address.
- Clues on Topics:
- Use the provided examples in Biology, Clinical Trials, Advertising Spend, Manufacturing, or formulate your own topic.
- Tailor your research objectives based on the chosen topic.
- Hypothesis Formulation:
- Clearly state your hypotheses following the structure provided in the examples.
- Results Interpretation:
- Apply hypothesis testing and confidence intervals to your data.
- Interpret the results derived from your analysis.
- Conclusions:
- Draw appropriate conclusions based on the interpreted results.
- Submission Guidelines:
- Submit a comprehensive report that includes data, analysis, interpretations, and conclusions.
- If working in a group, ensure that all group members' names are included on the submitted work.
This practical exercise aims to enhance your skills in hypothesis testing and confidence intervals within your field of study or personal interest. It encourages critical thinking, effective data analysis, and clear communication of research findings.
Some Suggested Useful Clues on Topics
Example 1: Biology
Hypothesis tests are often used in biology to determine whether some new treatment, fertilizer, pesticide, chemical, etc. causes increased growth, stamina, immunity, etc. in plants or animals.
For example, suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
If the p-value of the test is less than some significance level (e.g. α = .05), then she can reject the null hypothesis and conclude that the fertilizer leads to increased plant growth.
Example 2: Clinical Trials
Hypothesis tests are often used in clinical trials to determine whether some new treatment, drug, procedure, etc. causes improved outcomes in patients.
For example, suppose a doctor believes that a new drug is able to reduce blood pressure in obese patients. To test this, he may measure the blood pressure of 40 patients before and after using the new drug for one month.
He then performs a hypothesis test using the following hypotheses:
- H0: μafter = μbefore (the mean blood pressure is the same before and after using the drug)
- HA: μafter < μbefore (the mean blood pressure is less after using the drug)
If the p-value of the test is less than some significance level (e.g. α = .05), then he can reject the null hypothesis and conclude that the new drug leads to reduced blood pressure.
Example 3: Advertising Spend
Hypothesis tests are often used in business to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales.
For example, suppose a company believes that spending more money on digital advertising leads to increased sales. To test this, the company may increase money spent on digital advertising during a two-month period and collect data to see if overall sales have increased.
They may perform a hypothesis test using the following hypotheses:
- H0: μafter = μbefore (the mean sales is the same before and after spending more on advertising)
- HA: μafter > μbefore (the mean sales increased after spending more on advertising)
If the p-value of the test is less than some significance level (e.g. α = .05), then the company can reject the null hypothesis and conclude that increased digital advertising leads to increased sales.
If the p-value of the test is less than some significance level (e.g. α = .05), then the company can reject the null hypothesis and conclude that increased digital advertising leads to increased sales.
Example 4: Manufacturing
Hypothesis tests are also used often in manufacturing plants to determine if some new process, technique, method, etc. causes a change in the number of defective products produced.
For example, suppose a certain manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, they may measure the mean number of defective widgets produced before and after using the new method for one month.
They can then perform a hypothesis test using the following hypotheses:
- H0: μafter = μbefore (the mean number of defective widgets is the same before and after using the new method)
- HA: μafter ≠ μbefore (the mean number of defective widgets produced is different before and after using the new method)
If the p-value of the test is less than some significance level (e.g. α = .05), then the plant can reject the null hypothesis and conclude that the new method leads to a change in the number of defective widgets produced per month.
Example 5
You want to test whether there is a relationship between gender and height. Based on your knowledge of human physiology, you formulate a hypothesis that men are, on average, taller than women. To test this hypothesis, you restate it as:
- H0: Men are, on average, not taller than women.
Ha: Men are, on average, taller than women.