Two Sample Test

1. The Puromycin data frame has 23 rows and 3 columns of the reaction velocity versus substrate concentration in an enzymatic reaction involving untreated cells or cells treated with Puromycin.

• conc : a numeric vector of substrate concentrations (ppm)
• rate : a numeric vector of instantaneous reaction rates (counts/min/min)

• state: a factor with levels treated untreated

  Is there any mean population difference in values of rate and conc for two different treatments?

To start with we test for equality of variances

data(Puromycin)
var.test(Puromycin$rate ~ Puromycin$state)

    F test to compare two variances

data:  Puromycin$rate by Puromycin$state
F = 2.1026, num df = 11, denom df = 10, p-value = 0.2521
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.5737165 7.4131537
sample estimates:
ratio of variances 
          2.102622 

As p-value > 0.05, we do not reject H0

t.test(Puromycin$rate ~ Puromycin$state,var.equal=T)

    Two Sample t-test

data:  Puromycin$rate by Puromycin$state
t = 1.6112, df = 21, p-value = 0.1221
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -8.969925 70.682047
sample estimates:
  mean in group treated mean in group untreated 
               141.5833                110.7273 

As p-value > 0.05, we do not reject H0. Hence we conclude that rate may be equal for treated and untreated