The following data gave X- the water content of snow on April 1 and Y-the yield

Question

The following data gave X- the water content of snow on April 1 and Y-the yield from April to July (in inches) on the Snake River watershed in Wyoming for 1919 to 1935. (The data were taken from an article in Research Notes,Vol. 61, 1950, Pacific Northwest Forest Range Experiment Station, Oregon) X 23.1 32.8 31.8 32.0 30.4 24.0 | 39.5 24.2 52.5 | 37.9 30.5 25.1 12.4 35.1 31.5 21.1 27.6 y10.516.7 18.2 17.016.3 10.5 23.1 12.4 24.9 22.814.1 12.9 8.8 17.4 14.9 10.5 16.1 (a) Estimate the correlation between Y and X. Round your answer to 3 decimal places. (b) Test the hypothesis that Ho:=0 against H1:+0 with =0.05

Explanation / Answer

we can perform this in the open source statistical package R , the snippet is as folllows

x <- c(23.1,32.8,31.8,32,30.4,24,39.5,24.2,52.5,37.9,30.5,25.1,12.4,35.1,31.5,21.1,27.6)
y <-c(10.5,16.7,18.2,17,16.3,10.5,23.1,12.4,24.9,22.8,14.1,12.9,8.8,17.4,14.9,10.5,16.1)

## correlation
cor(x,y)

## cor.test

cor.test(x,y)

The results are

> cor(x,y)
[1] 0.9332029

> cor.test(x,y)

   Pearson's product-moment correlation

data: x and y
t = 10.058, df = 15, p-value = 4.632e-08 as the p value is less than 0.05 , hence the result is signficant and we reject the null hypothesis in favor of alternate hypothesis

alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.8206532 0.9760508 ## also the 95% CI does not contain zero , hence the result is significant
sample estimates:
cor
0.9332029

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