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If the average rainfall in a given area is 8 inches and the following table represents the average rainfall for four consecutive years, then the value of test statistic 't' is_____.

Yearyear 1year 2Year 3year 4
Rainfall (inches)8565

Solution

✅ Correct Option: 4

xˉ=8+5+6+54=6\bar{x}=\frac{8+5+6+5}{4}=6; deviations 2,−1,0,−12,-1,0,-1 give ∑d2=6\sum d^2=6, so s2=63=2s^2=\frac{6}{3}=2 and s=2s=\sqrt2.

t=xˉ−μs/n=6−82/2=−22=−2.828t=\frac{\bar{x}-\mu}{s/\sqrt n}=\frac{6-8}{\sqrt2/2}=-2\sqrt2=-2.828.

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