7.3

7.3 Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day. The numbers in the table represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Test at the 5% level. Dolphin Activity Activity Period Row Morning Noon Afternoon Evening Total Trave 6 14 13 39 Feed 28 56 83 SociE 3.8 9 10 62 Column Total 15 23 79 189 . This is Chi-Square test for independence. . All given numbers are Observed values ( O ). Put them in one column. . Create a column for Expected values ( E ). The Rule is: for each Observed Value multiply Row Total (RT) by Column Total (CT) and divide by all total (189) : E = (RTxCT)/189 For example. for Morning Travel (6] Expected value will be: E = (39/189)x72 = 14.9 for Morning Feed (28) Expected value will be: E = (88/189)x72 = 33.5 for Noon Social (5) Expected value will be: E = (62/189)x15 = 4.9 for Evening Feed (56) Expected value will be: E = (88/189)x79 = 36.8 E O -E (0- E) (0- E)E 6 14.9 33.5 6 4.9 14 13 SE 36.8. Complete the E-column . Complete the rest of the table. . Chi-Square * is the total of the last column . Use online Chi-Square calculator: https://www.socscistatistics.com/pvalues/chidistribution.aspx and find p-value. Degree of Freedom for given data is (4-1)(3-1] = 6. . Compare p-value to @ = 0.05 and make the conclusion