The average Jamaican’ male height is 5 ft 8 inches (173 cm) whereas the average Jamaican female height is 5ft 3 inches (160 cm). Moreover, a male height of 6 ft 1 inch (185 cm) is considered tall, and a height of 5 ft 7 inches (170 cm) is considered tall in women. On the other hand, a male height of 5 ft 5 inches (165 cm) and shorter is considered short whereas, women heighted 5 feet (152 cm) or shorter are considered short. a. Is there a notable difference between males and females in the Jamaican population?
1. Write the null and alternative hypotheses. [2]
2. What is your alpha level? [1]
3. Determine the range needed for each gender (Example: Male = 160-187 cm; Female = 150-173 cm) and use the range to conduct 10 imaginary experiments with 15 subjects in every list (male/female). Note: It is okay to use larger/smaller samples for each experiment. [10]
4. Use a student’s t-test in excel (data analysis) to test your hypothesis at the given alpha level for each imaginary experiment. [10]
5. Determine the number of successes (5/10 = 50%) and state whether you think you have enough power to conduct the experiment. [2]
The Correct Answer and Explanation is:
To analyze the notable difference between male and female heights in the Jamaican population, we will outline and explain each step systematically.
1. Null and Alternative Hypotheses
- Null Hypothesis ((H_0)): There is no significant difference between the average heights of males and females in the Jamaican population. ((H_0: \mu_{\text{male}} = \mu_{\text{female}}))
- Alternative Hypothesis ((H_a)): There is a significant difference between the average heights of males and females in the Jamaican population. ((H_a: \mu_{\text{male}} \neq \mu_{\text{female}}))
2. Alpha Level
Set the significance level ((\alpha)) at 0.05 (5%), which is standard in most statistical tests.
3. Height Range and Imaginary Experiments
- Male height range: 165–185 cm
- Female height range: 152–170 cm
For 10 imaginary experiments, randomly generate height data for 15 subjects for each gender. Use the given range to create samples in Excel or manually by picking random numbers within the ranges.
Example Male List: {165, 170, 172, 175, 180, 185, …}
Example Female List: {152, 155, 158, 160, 165, 170, …}
4. Conduct a Student’s t-test
- Use Excel’s Data Analysis tool.
- Select “t-Test: Two-Sample Assuming Equal Variances.”
- Input male and female height data from each experiment.
- Note the p-value for each test.
5. Number of Successes and Power Analysis
Count how many experiments have a p-value < 0.05 (successes). If at least 5 out of 10 experiments (50%) show significance, we can tentatively conclude there is a notable difference.
Explanation
By comparing the p-values to the alpha level, we evaluate if the null hypothesis can be rejected. A sufficient number of significant results (e.g., (>50\%)) provides initial support for the hypothesis. However, if variability is high or the sample size is small, the statistical power may not be adequate. Larger sample sizes or more experiments are recommended to ensure robustness and reproducibility.