02 May At A= 0.05, Use The Table To Test The Hypothesis That The Ratio Of Length And Breadth For These Sample Lakes Is 1.618 …
Hemishpere Lake Length Breadth
East Lake Toba 62 18
West Okeechobee 33 30
West tahoe 22 12
East Eyre South 40 15
East eyre north 89 48
West Champlain 120 12
West Superior 350 160
West Michigan 306 118
East Orumieh 87 34
East Tanganyika 420 31
East caspian sea 745 300
East victoria 209 160
West clear lake 19 8
West flathead 27 16
West Great Bear 190 110
East Baikal 395 30
East nyasa 360 47
West Ontario 193 53
East Geneva 45 9
West Winnepeg 265 70
a. The golden ratio = 1.618 is thought to be a “natural” relationship between length and breadth. At a= 0.05, use the table to test the hypothesis that the ratio of length and breadth for these sample lakes is 1.618
b. Similarly, test the hypothesis that the ratio is bigger than 2.26
c. correlate “length” versus “breadth”. Compute the line of regression. Graph it
d. Divide the lakes into western and eastern hemispheres. Test the hypothesis that their ratios have the same sample means. Discuss the viability of that hypothesis, in light of your analysis.
e. Global warming is creating a new great lake. Suppose the length is 260 miles. Give a 90% confidence interval for the breadth of this new lake. Use a t-statistic.
f. Test the independence of the length and breadth variables using a chi-square test with a=0.05
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