Test the hypothesis: additional work affects productivity of yields, i.e. g.
The test data is defined as:(Without additional work / with additional work) $\ 93.8;88 99;95.2 95.4;86 80.8;77 86.7;88.5 98.3;94.5 98.6;94.9 94.6;88.3 89;93.1 95.7;95 97.2;91.7 96.7;82.8 90.3;90.8 85.8;79.5 95.9;81 91.3;89$
I tried to solve this task with R:
> a = c(93.8,99,95.4,80.8,86.7,98.3,98.6,94.6,89,95.7,97.2,96.7,90.3,85.8,95.9,91.3)
> b = c(88,95.2,86,77,88.5,94.5,94.9,88.3,93.1,95,91.7,82.8,90.8,79.5,81,89)
> var.test(a,b, var.equal=TRUE, alt="greater")
F test to compare two variances
data: a and b
F = 0.82018, num df = 15, denom df = 15, p-value = 0.647
alternative hypothesis: true ratio of variances is greater than 1
95 percent confidence interval:
0.3412518 Inf
sample estimates:
ratio of variances
0.8201807
The $ p-value $ is greater than $ .05 $ si I can't reject the $H_{0}$ hypothesis that $ \mu = \mu_{0}$. Is this correct?