Question

The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern, measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges from o (less empathetic) to 28 (more empathetic). The following data, representing random samples of 14 males and 14 females, are consistent with results reported in psychological studies. Boxplots show that it is reasonable to assume that the populations are approximately normal. Can you conclude that there is a difference in mean empathy score between men and women? Let #, denote the mean empathy score for men. Use the a = 0.05 level and the P- value method with the T1-84 Plus calculator 13 8 20 15 Males 12 16 13 26 21 23 18 23 15 23 13 8 20 15 Females 22 20 26 25 28 24 21 23 15 26 1925 16 19

Answer 1

Using a TI-84 Plus calculator, one conducts a two-sample t-test to determine if there's a significant difference in mean empathy scores between males and females. With the given α = 0.05 and the data entered into the calculator, the P-value obtained determines whether to reject or not reject the null hypothesis.

Step-by-step explanation:

To determine if there is a difference in mean empathy scores between men and women using the Interpersonal Reactivity Index, we need to conduct a two-sample t-test. The given data samples are for 14 males and 14 females, and with an α = 0.05 (or 5%) level of significance, we will use the P-value method with a TI-84 Plus calculator to perform the test. Assuming that the populations are approximately normal based on the boxplot information, here is the step-by-step process:

Enter the male empathy scores into one list (L1) and the female scores into another list (L2) on the TI-84 Plus.

Access the STAT TESTS menu and select '2-Sample T-Test.'

Set the input to 'Data' and specify L1 and L2 for the two groups. Also, set 'Pooled' to 'NO' because we do not assume equal variances.

Choose ‘Calculate’ and press ENTER.

Review the output for the test statistic (t), degree of freedom (df), and the P-value.

If the P-value is less than the significance level of 0.05, we reject the null hypothesis, suggesting that there is a statistically significant difference in mean empathy scores between men and women.

If the P-value is greater than 0.05, we fail to reject the null hypothesis, indicating no significant difference in the mean empathy scores.

Remember, a lower P-value indicates stronger evidence against the null hypothesis, while a higher P-value indicates weaker evidence.