Question

Question 3 of 10 (1 point) | Attempt 1 of Unlimited View question in a popup 11.1 Section Exercise 17 (p-value, calc) Empathy: 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 0 (less empathetic) to 28 (more empathetic). The following data, representing random samples of 15 males and 15 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 u, denote the mean empathy score for men. Use the a = 0.05 level and the P-value method with the TI-84 Plus calculator. Males 13 20 12 16 13 26 21 23 8 25 15 23 17 22 15 ol. Females . 22 20 26 25 28 24 16 19 20 23 23 15 26 19 25 Send data to Excel

Answer 1

Hypotheses : To test null hypothesis Ho :M1 - M2 = 0 against alternative hypothesis H1 :M1-M2 > 0 This is a one tailed right sided test as the alternative hypothesis contains '>' sign. Here, 21 = 48.10, si = 14.20, ni - 10,72 = 40.08, S2 = 13.32, n2 = 12 The test statistic can be written as: (C1 – 22) - 0 t= + ni n2 which under Ho follows a t distribution with 18 df. where .)2 14.202 10 + 13.32 )? ni n2 df 18 II 14.202 12 13.322 12 12-1 10 10-1 + ni-1 n2-1 and standard error for the difference between means SE= 14.202 10 + 13.322 12 5.912730 ni n2

Decision rule / Rejection region : We reject Ho at 0.05 level of significance if P-value < 0.05 or if tstat > t0.05,df 0.4 - 0.3- density 0.2- 0.1- 0.0- -4 1 0 -2 2 4 t Now, Value of the test statistic: The value of the test statistic is (48.10 – 40.08) tstat = = 1.355832 ~1.356 14.202 10 + 13.322 12 associated degrees of freedom = 18 The critical value = tcritical to.05,18 =1.734064 = 1.734 P - value = P(t18 > tstat) = P(t18 > 1.355832) = 1- P(t18 < 1.355832) = 1 – 0.904040 = 0.095960 ~ 0.0960 Conclusion : Since p-value > 0.05 and tstat * tcritical = 1.734, so We fail to reject Ho at 0.05 level of significance Hence, we can conclude that mean for first population is not significantly greater than the mean for second population.

There is not sufficient evidence to conclude that there is significant difference in mean empathy score between men and women.