Question

A data set was collected.

  4.7 2 2.6 4.2 6 4.1 3.9 3.8 3.3 3.9 3.8 4 3.5 3.8 3.6 4.4 4.4 3.3 6 5.4

Determine whether we can consider that this sample is from a normal distribution.

Answer 1

We do the test for normality of the given data using two methods implementing in R.

i) Shapiro Wilk's test for Normality

ii) Quantile-Quantile plot.

i) For Shapiro Wilk's test for Normality, we use the R code given below.

x=c(4.7,2,2.6,4.2,6,4.1,3.9,3.8,3.3,3.9,3.8,4,3.5,3.8,3.6,4.4,4.4,3.3,5.4)

shapiro.test(x)

The output screen is given below:

> x=c(4.7,2,2.6, 4.2,6, 4.1,3.9,3.8.3.3, 3.9,3.,4.3.5,3.8, 3.6,4.4.4.4,3.3,5.4) > shapiro.test (x) Shapiro-Wilk normality test data: W = 0.95267, p-value 0.4382

Clearly the p-value is 0.4382, which is very high and greater than any standard level of significance (0.05), so we accept the null hypothesis that the data is a sample from a Normal distribution.

So we can definitely consider this data as a sample from a Normal distribution.

ii) For Q-Q plot of normality, we use the following R code.

qqnorm(x)

The output plot is given below:

From the plot, the points forms almost a straight line like y=x

RGUI (64-bit R KR Graphics: Device 2 (ACTIVE) Normal Q-Q Plot 6 o 5 O O Sample Quantiles 4 3 2. -2. -1 0 1 2 Theoretical Quantiles

So we can conclude that the data is highly normal.

So we can definitely consider this data as a sample from a Normal distribution.