Question

An analyst is comparing the rice production in two countries. The analyst claims that the variation in wheat production is less in county 2 than in county 1. A sample of 41 growers in country 1 had a standard deviation of 0.65 bushels per acre. A sample of 31 growers in country 2 had a standard deviation of 0.58 bushels per acre. At α = 0.05, can you support the analyst’s claim?

Answer 1

Given that

standard deviation for country 1, s1 = 0.65 and n1 = 41 (sample size)

standard deviation for country 2, s2 = 0.58 and n2 = 31 (sample size)

We have to test the claim that the variation in wheat production is less in county 2 than in county 1

test statistic = F = s1^2/s2^2

= 0.65^2/0.58^2

= 1.256

degree of freedom numerator = n1-1 =41 - 1 = 40

degree of freedom denominator = n2 -1 =31 -1 = 30

using F distribution table for df1 = 40, df2 = 30 with test statistic 1.256

we get

p value = 0.2605

p value is greater than 0.05 significance level, so we failed to reject the null hypothesis

therefore, we can say that there is insufficient evidence to conclude that the variation in wheat production is less in county 2 than in county 1