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Chapter 10: Q. 11 (page 446)

Ecosystem Response. Refer to Problem 10, and find a 90% confidence interval for the difference in the mean lengths of time that ice stays on the two lakes. Interpret your result.

Short Answer

Expert verified

(-3.3752,6.1252)

Step by step solution

01

Given Information

n=Sample Size =8

c=Confidence level =90%=0.90

02

Explanation

Here, the difference among each pair of values is needed to be calculated as follows:

d¯=Sample Mean=12+7+1+0-11+0-11+0+6-48≈1.375

Sd=Sample standard deviation

=(12-1375)2+…+(-4-1.375)28-1≈7.09

Calculate the critical value with df=n-1=8-1=7

t*=1.895

Then, the margin of error is

E=t*×sdn=1.895×7.098≈4.7502

The confidence interval's endpoints are:

d¯-E=1.375-4.7502=-3.3752

d¯+E=1.375+4.7502=6.1252

It can be said with 90%confidence that the difference in mean length of time that ice stays on the Mendota lake is between 3.3752days lesser and 6.1252days greater than the mean length of time that ice stays on the Monona lake.

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Most popular questions from this chapter

Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the pairedt -test, the paired Wilcoxon signed-rank test, or neither of these tests if preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is

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