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Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities...

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Researchers watched groups of dolphins off the coast of Ireland in1998 to determine what activities the dolphins partake in atcertain times of the day (\"Activities of dolphin,\" 2013). Thenumbers in Table 3 represent the number of groups of dolphins thatwere partaking in an activity at certain times of days. Is thereenough evidence to show that the activity and the time period areindependent for dolphins? Why or Why not? Test at the 1% level.


ActivityMorningNoonAfternoonEveningRow Total
Travel66141339
Feed28405688
Social38591062
Column Total72152379189

Answer & Explanation Solved by verified expert
4.4 Ratings (849 Votes)

Ans:

H0:the activity and the time period are independent for dolphins.

Ha:the activity and the time period are dependent for dolphins.

Observed(fo)
Activity Morning Noon Afternoon Evening Row Total
Travel 6 6 14 13 39
Feed 28 4 0 56 88
Social 38 5 9 10 62
Column Total 72 15 23 79 189
Expected(fe)
Activity Morning Noon Afternoon Evening Row Total
Travel 14.86 3.10 4.75 16.30 39
Feed 33.52 6.98 10.71 36.78 88
Social 23.62 4.92 7.54 25.92 62
Column Total 72 15 23 79 189
Chi square=(fo-fe)^2/fe
Activity Morning Noon Afternoon Evening Row Total
Travel 5.28 2.73 18.04 0.67 26.72
Feed 0.91 1.28 10.71 10.04 22.93
Social 8.76 0.00 0.28 9.77 18.81
Column Total 14.95 4.00 29.03 20.48 68.46

Test statistic:

Chi square=68.46

df=(3-1)*(4-1)=6

alpha=0.01

critical chi square value=CHIINV(0.01,6)=16.812

As,test statistic chi square is greater than critical chi square value,so reject the null hypothesis.

There is not enough evidence to conclude that the activity and the time period are independent for dolphins.
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