Several farmers were interested in the relationship between the mean temperature

Question

Several farmers were interested in the relationship between the mean temperature and the rainfall in July and the output of sugar beets. The following data for the last ten years was collected at a certain farm; Production (metric tons) Temperature 426.3 471.6 507.9 432.6 553.5 498.8 571.4 580.5 589.6 462.3 15 18.5 17.2 15.5 18.1 16.1 16.6 17.8 16.1 14.4 Rainfall (cm 8.3 10.5 8.2 9.5 7.8 10.1 10.8 9.3 7.5 10.8 a) At the 5% level of significance, can we conclude that the average temperature in July was less than 17 °C? What is the p-value? b) At the 1% level of significance, can we conclude that the average rainfall in July is more than 9cm? What is the p-value? c) Derive a 95% confidence interval for the average production of beets d) Can we conclude that the production of beets is higher when the average temperature in July is above 165 °C? use a 5% level of significance

Explanation / Answer

Enter the data in Excel and save it as .csv file.

> data1=read.csv(file.choose(),header=T) #importing csv file into R
> data1
production temp rainfall
1 426.3 15.0 8.3
2 471.6 18.5 10.5
3 507.9 17.2 8.2
4 432.6 15.5 9.5
5 553.5 18.1 7.8
6 498.8 16.1 10.1
7 571.4 16.6 10.8
8 580.5 17.8 9.3
9 589.6 16.1 7.5
10 462.3 14.4 10.8
> attach(data1)

a) #One-sample t-test
> t.test(temp,mu=17,alt="l")

One Sample t-test

data: temp
t = -1.0904, df = 9, p-value = 0.1519
alternative hypothesis: true mean is less than 17
95 percent confidence interval:
-Inf 17.32013
sample estimates:
mean of x
16.53
Since p-value >0.05, we accept the null hypothesis and conclude that the temperature is not significantly less than 17.

b)
> t.test(rainfall,mu=9,alt="g",conf.level=0.99)

One Sample t-test

data: rainfall
t = 0.70205, df = 9, p-value = 0.2502
alternative hypothesis: true mean is greater than 9
99 percent confidence interval:
8.154721 Inf
sample estimates:
mean of x
9.28
Since p-value>0.05, we accept the null hypothesis and conclude that the rainfall is not significantly greater than 9cm.

c)
> t.test(production)

One Sample t-test

data: production
t = 26.272, df = 9, p-value = 8.098e-10
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
465.584 553.316
sample estimates:
mean of x
509.45

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