MAS183 Statistical Data Analysis
Assessment 3
Student name Student number
- -
Question 1
• Null Hypothesis (H0): No association between dolphin activity and time of day
• Alternative Hypothesis (H1): An association between dolphin activity and time of day
Activity\Time Morning Afternoon Evening TOTAL
Travelling 7 21 12 40
Feeding 27 3 55 85
Socialising 37 13 11 61
TOTAL 71 37 78 186
➢ Expected counts: row total x column total / grand total
Activity\Time Morning Afternoon Evening TOTAL
Travelling 15.26882 7.9569892 16.7741935 40
Feeding 32.44624 16.908602 35.6451613 85
Socialising 23.28495 12.134409 25.5806452 61
TOTAL 71 37 78 186
➢ Test statistic: (observed – expected)2 / expected
Activity\Time Morning Afternoon Evening TOTAL
Travelling 4.477972 21.379962 1.35880893 27.2167433
Feeding 0.914174 11.440876 10.5094147 22.8644639
Socialising 8.078297 0.0617458 8.31078388 16.4508262
TOTAL 13.47044 32.882584 20.1790075 66.5320333
• Test statistic: 66.532
• Degrees of freedom: (3-1)(3-1) = 4
• Chi-square value: 13.277 (from tables) where α = 0.01 and df = 4
• Conclusion: the test statistic is greater than the chi-square value, so we can reject the null
hypothesis. There is strong evidence to suggest that dolphin activity varies during the day, and
there is a significant association between the activities and the time of day they were
observed.
Question 2
a. The predictor (independent) variable is the temperature, and the response (dependent)
variable is the ice-cream. This is because the number of ice-creams made depends on the
temperature.
b. i. Graphs pictured on next page
Assessment 3
Student name Student number
- -
Question 1
• Null Hypothesis (H0): No association between dolphin activity and time of day
• Alternative Hypothesis (H1): An association between dolphin activity and time of day
Activity\Time Morning Afternoon Evening TOTAL
Travelling 7 21 12 40
Feeding 27 3 55 85
Socialising 37 13 11 61
TOTAL 71 37 78 186
➢ Expected counts: row total x column total / grand total
Activity\Time Morning Afternoon Evening TOTAL
Travelling 15.26882 7.9569892 16.7741935 40
Feeding 32.44624 16.908602 35.6451613 85
Socialising 23.28495 12.134409 25.5806452 61
TOTAL 71 37 78 186
➢ Test statistic: (observed – expected)2 / expected
Activity\Time Morning Afternoon Evening TOTAL
Travelling 4.477972 21.379962 1.35880893 27.2167433
Feeding 0.914174 11.440876 10.5094147 22.8644639
Socialising 8.078297 0.0617458 8.31078388 16.4508262
TOTAL 13.47044 32.882584 20.1790075 66.5320333
• Test statistic: 66.532
• Degrees of freedom: (3-1)(3-1) = 4
• Chi-square value: 13.277 (from tables) where α = 0.01 and df = 4
• Conclusion: the test statistic is greater than the chi-square value, so we can reject the null
hypothesis. There is strong evidence to suggest that dolphin activity varies during the day, and
there is a significant association between the activities and the time of day they were
observed.
Question 2
a. The predictor (independent) variable is the temperature, and the response (dependent)
variable is the ice-cream. This is because the number of ice-creams made depends on the
temperature.
b. i. Graphs pictured on next page
