Stat. 316: Hypothesis Testing

Hypothesis Testing - Two Independent Samples

Sixteen mice were randomly assigned to a treatment group or a control group. Shown are their survival times in days, following a test surgery. Did the treatment prolong suvivial times?

Group	Data
Treatment	94 197 16 38 99 141 23
Control	52 104 146 10 50 31 40 27 47

Enter the data.

Notice that the Treatment has a much higher median than the Control group.

treatment <- c(94, 197, 16, 38, 99, 141, 23)

control <- c(52, 104, 146, 10, 50, 31, 40, 27, 47)

boxplot(treatment, control, names = c("Treatment", "Control"))

Perform a two-sample t-test.

\(H_0: \mu_1 = \mu_2\)

\(H_a: \mu_1 > \mu_2\)

t.test(treatment, control, alternative = "greater")

    Welch Two Sample t-test

data:  treatment and control
t = 1.0554, df = 9.6409, p-value = 0.1585
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 -22.09459       Inf
sample estimates:
mean of x mean of y 
 86.85714  56.33333 

Since the \(p \mbox{-} value = 0.1585 > 0.05\), we fail reject the null hypothesis. There is insufficent evidence that the treatment prolongs survival times.