Question

The sample data in the table below shows Blood Alcohol Concentration (BAC) level at arrest of randomly selected jail inmates who were convicted of DWI or DUI offences. The data are categorized by the type of drink consumed (based on data from U.S. Department of Justice). At the 0.05 level of significance, test the claim that beer drinkers and liquor drinkers have the same BAC levels.

Beer	0.129	0.154	0.203	0.146	0.155	0.190	0.148	0.187	0.164	0.152	0.212	0.165
Liquor	0.220	0.253	0.247	0.190	0.225	0.241	0.224	0.257	0.185	0.227	0.226	0.182	0.205	0.234

a) Identify the appropriate nonparametric test. What will be an equivalent parametric test?

b) State the hypotheses.

c) Find the critical value (s). State the assumptions that were made in performing this test.

Answer 1

(a) PARAMETRIC TEST- unpaired t-test

NON-PARAMETRIC EQUIVALENT - Mann Whitney U test

(b)

The null hypothesis for the independent t-test is that the population means from the two unrelated groups are equal:

H₀: u₁ = u₂

ALTERNATE HYPOTHESIS:-

the population means are not equal:

H_A: u₁ ? u₂

_(c)

Equation

Difference Scores Calculations

Treatment 1

N₁: 12
df₁ = N - 1 = 12 - 1 = 11
M₁: 0.17
SS₁: 0.01
s²₁ = SS₁/(N - 1) = 0.01/(12-1) = 0


Treatment 2

N₂: 14
df₂ = N - 1 = 14 - 1 = 13
M₂: 0.22
SS₂: 0.01
s²₂ = SS₂/(N - 1) = 0.01/(14-1) = 0


T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((11/24) * 0) + ((13/24) * 0) = 0

s²_M1 = s²_p/N₁ = 0/12 = 0
s²_M2 = s²_p/N₂ = 0/14 = 0

t = (M₁ - M₂)/?(s²_M1 + s²_M2) = -0.06/?0 = -5.7

The t-value is -5.69953. The p-value is < .00001. The result is significant at p < .05.

So accept null hypothesis. So beer drinkers and liquor drinkers have the same BAC levels.

df=n1 + n2 ? 2 = 12+14-2 =24

t-value (two-tailed):+/- 2.06389857

assumptions

• Independent observations. ...
• Normality: the dependent variable must follow a normal distribution in the population.
• Homogeneity: the standard deviation of our dependent variable must be equal in both populations.