6

Question 1: Aspirin Concentration

Hypotheses

• H0: µA = µB (the mean concentrations of Aspirin A and B are the same)
  
• H1: µA ≠ µB (the mean concentrations are different)

Paired t-test

Q1.1-Test the hypothesis using a paired t-test, report the p-value and state your conclusion (alpha = 0.05) ?

aspirinA <- c(15,26,13,28,17,20,7,36,12,18)
aspirinB <- c(13,20,10,21,17,22,5,30,7,11)

paired_test <- t.test(aspirinA, aspirinB, paired = TRUE)
paired_test

## 
##  Paired t-test
## 
## data:  aspirinA and aspirinB
## t = 3.6742, df = 9, p-value = 0.005121
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  1.383548 5.816452
## sample estimates:
## mean difference 
##             3.6

• Since p < 0.05, we reject H0. The mean concentrations of Aspirin A and B are significantly different.

Q1.2-Suppose that you tested this hypothesis using a two-sample t-test (instead of a paired t-test).  What would the p-value of your test have been?

independent_test <- t.test(aspirinA, aspirinB, paired = FALSE)
independent_test

## 
##  Welch Two Sample t-test
## 
## data:  aspirinA and aspirinB
## t = 0.9802, df = 17.811, p-value = 0.3401
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -4.12199 11.32199
## sample estimates:
## mean of x mean of y 
##      19.2      15.6

• Since p > 0.05, we reject Ha. The mean concentrations of Aspirin A and B are significantly the same.

Q2-Walking time

Q2.1- Hypotheses

• H0: The average walking time is the same for both groups.
• H1: The average walking time is less for the exercise group.

Q2.2- Why we used non-parametric?

The sample size is small (n=6 per group) and the data might not be normal. That’s why we use the non-parametric Mann-Whitney U Test.

Q2.3- Mann-Whitney U Test?

exercise <- c(9.50, 10.00, 9.75, 9.75, 9.00, 13.0)
no_exercise <- c(11.50, 12.00, 13.25, 11.50, 13.00, 9.00)

wilcox.test(exercise, no_exercise, alternative = "less")

## Warning in wilcox.test.default(exercise, no_exercise, alternative = "less"):
## cannot compute exact p-value with ties

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  exercise and no_exercise
## W = 9, p-value = 0.08523
## alternative hypothesis: true location shift is less than 0

Since the p-value (0.08523) is greater than the alpha (0.05), we fail to reject the null hypothesis (H0). => There is insufficient evidence to support the claim that active exercise reduces the time it takes for infants to learn to walk alone.