Biologists Studying the Ecology of an Island - Science and Maths Assignment Help

Assignment Task:

Task:

Question 1 [(3+1+2+1=7) marks] 
Biologists studying the ecology of an island off the coast of Ecuador have noticed that a particular population of birds have lost the ability to fly. This may be due to successive generations living in a location without predators, which differs from the mainland. In 2019 the biologists measured the wingspan of 150 of these birds. They believe that the average wingspan in 2019 is significantly lower than the standard wingspan of 48 cm. A t-test is performed and, at a significance level of 0.01, a p-value of 0.0062 is determined.

(a) State the null and alternate hypotheses using statistical notation. Define any variables used.

(b) Is this a one-tailed, two-tailed, or 150-tailed test?

(c) What decision would you make regarding the null hypothesis? Please provide your reasoning.

(d) What conclusion can be drawn from this statistical test? 
 

Question 2 [(2+2+2+1+1=8) marks] 
During winter, the surface of Lake Superior, USA, freezes. Over six winters, a climate scientist recorded the daily minimum temperature at Lake Superior and on each mid-winter's day he measured the thickness of surface ice. The graph below shows the relationship between average minimum winter temperature (°C) of the Lake Superior area and thickness of surface ice (cm). 
Thickness of surface ice on Lake Superior, USA, in various average minimum winter temperatures 250 
• 200 
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• 150 
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100 
-25 -20 -15 -10 -5 Average minimum winter temperature (°C) 
o 
(a) From the graph shown, describe and justify any relationship that exists between the two variables. (b) The regression equation for the collected data is S = 28.3— 8.5T . Where S is the Thickness of surface ice (cm) and T is the Average minimum winter temperature (°C) of the Lake Superior area. What is the slope of the regression equation? Interpret its meaning in this context. (c) Using the regression equation shown in part (b), predict the thickness of surface ice (cm) when the average minimum winter temperature is -12°C. (d) The Pearson correlation coefficient for this data is r = 0.96. What does this correlation coefficient value tell us about the relationship between the two variables in this case? (e) Comment on the appropriateness of using the regression equation to predict ice thickness when average min. winter temperature is -5°C. 
 

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