A researcher plans to use a sample of 500 men and women attending a well-known online university to study the relationship between the number of fast-food hamburgers consumed in a month and BMI (body mass index). The null hypothesis is that there is no relationship between fast-food hamburger consumption and BMI.
A description the statistical test the researcher would use to test the null hypothesis
The researcher can use a statistical test called correlation analysis to test the null hypothesis that there is no relationship between fast-food hamburger consumption and BMI. Correlation analysis is used to examine the strength and direction of the relationship between two continuous variables.
To perform the correlation analysis, the researcher needs to collect data on the number of fast-food hamburgers consumed in a month and the BMI of the 500 men and women attending the online university. The number of fast-food hamburgers consumed and BMI are both continuous variables, which means they can take any value within a certain range.
Once the data is collected, the researcher can calculate the correlation coefficient, which measures the strength and direction of the relationship. The most commonly used correlation coefficient is Pearson's correlation coefficient (r), which ranges from -1 to +1. A value of +1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 indicates no relationship.
To test the null hypothesis, the researcher can use a significance test on the correlation coefficient. This test determines whether the observed correlation coefficient is statistically significant, indicating that the relationship between fast-food hamburger consumption and BMI is unlikely to occur by chance.
The researcher would set a significance level (usually denoted as alpha) to determine the threshold below which the correlation coefficient would be considered statistically significant. Common significance levels include 0.05 and 0.01.
If the calculated correlation coefficient falls below the significance level, the researcher can reject the null hypothesis and conclude that there is evidence of a relationship between fast-food hamburger consumption and BMI. On the other hand, if the calculated correlation coefficient is not statistically significant, the researcher would fail to reject the null hypothesis and conclude that there is no evidence of a relationship between the two variables.
In summary, the researcher would use correlation analysis, specifically Pearson's correlation coefficient, to test the null hypothesis that there is no relationship between fast-food hamburger consumption and BMI.