Question

do vegetarians and meat-eaters differ in their levels of intelligence? you randomly select 60 vegetarians and 60 meat-eaters and give them all a test of intelligence. what test will tell you if there is a significant difference between these two groups in terms of intelligence?

Answer 1

To assess if there's a difference in intelligence between vegetarians and meat-eaters, an independent samples t-test is used. This test examines the means of two independent samples for a significant difference. Conducting the test involves checking for normality, calculating the t-statistic, and comparing the p-value to the significance level.

Step-by-step explanation:

To determine if there is a significant difference in levels of intelligence between vegetarians and meat-eaters, the appropriate statistical test to use is the independent samples t-test. This test compares the means of two independent groups to see if there is a statistically significant difference between them. Since intelligence scores are typically interval/ratio level data and the two groups are independent of one another, the assumptions for conducting a t-test are met. Additionally, you would want to ensure that the data is approximately normally distributed and that there is homogeneity of variances between the two groups before conducting the t-test. If these assumptions are not met, you might consider using a non-parametric alternative, such as the Mann-Whitney U test.

The steps to conduct an independent samples t-test are as follows:

1. Formulate the null hypothesis (H0) that there is no difference in intelligence scores between vegetarians and meat-eaters, and the alternative hypothesis (H1) that there is a difference.
2. Collect intelligence test scores from the two groups.
3. Check for assumptions: normality and homogeneity of variance.
4. Conduct the t-test to calculate the t-statistic and the p-value.
5. Compare the p-value against the chosen level of significance (commonly 0.05) to determine if the results are statistically significant.

If the p-value is less than the significance level, you reject the null hypothesis and conclude that there is a significant difference between the two groups. If the p-value is greater than the significance level, you fail to reject the null hypothesis, indicating that there is no evidence of a significant difference in intelligence between vegetarians and meat-eaters.