QUESTION 5:

female <- c(0.588, 0.546, 0.452, 0.646, 0.380, 0.434, 0.613,
            0.652, 0.340, 0.491, 0.518, 0.403, 0.566, 0.516, 
            0.442, 0.636, 0.545, 0.377, 0.617, 0.481)


male <- c(0.375, 0.654, 0.374, 0.373, 0.224, 
          0.256, 0.563, 0.465, 0.488, 0.477,
          0.427, 0.405, 0.402, 0.337, 0.655)

-> Part a)

  1. For test, use shapiro-wilk test.
shapiro.test(female)
## 
##  Shapiro-Wilk normality test
## 
## data:  female
## W = 0.95448, p-value = 0.4401

Since the p-value is bigger than 0.05 we fail to reject H0, so it is normally distributed.

shapiro.test(male)
## 
##  Shapiro-Wilk normality test
## 
## data:  male
## W = 0.95006, p-value = 0.5253

Since the p-value is bigger than 0.05 we fail to reject H0, so it is normally distributed.

  1. For plot use histogram.
hist(female, main="Histogram for Female", xlab = "Values", ylab = "Frequency")

hist(male, main="Histogram for Male", xlab = "Values", ylab = "Frequency")

-> Part b)

µf = Reaction time for females.

µm = Reaction time for males.

H0: µf = µm

H1: µf != µm

-> Part c)

H0: σ2 f = σ2 m

H1: σ2 f != σ2 m

var.test(female, male, alternative = "two.sided", ratio=1)
## 
##  F test to compare two variances
## 
## data:  female and male
## F = 0.60404, num df = 19, denom df = 14, p-value = 0.3032
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2111494 1.5988494
## sample estimates:
## ratio of variances 
##          0.6040397

-> Part d)

Since the alpha = 0.05 and p-value = 0.3032, we have

p-value > alpha , so fail to reject H0 . The variances are not equal.

-> Part e)

Population variances are unknown and sample size is small, use t-test.

ttest <- t.test(alternative = "two.sided", female, male, var.equal = FALSE)
ttest$conf.int
## [1] 0.0007052296 0.1602614371
## attr(,"conf.level")
## [1] 0.95

-> Part f)

Since the confidence interval do not include zero, we reject H0 , so there is enough evidence to say that the mean values for female and male reaction times are differ from each other.