unit 10 .- parametric tests. - OpenCourseWare de la Universidad de

STATISTICAL METHODS FOR BUSINESS
UNIT 10 .- PARAMETRIC TESTS.
10.1 .- Tests for the mean.
10.2 .- Tests for the proportion.
10.3 .- Tests for the variance.
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
UNIT 10. GOALS
• Solve statistical testing problems for the
mean, proportion and variance.
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
One-tailed test for the mean
H0 : µ ≥ µ0
H1 : µ < µ0
•P-VALUE APPROACH
d
• Obtain the test statistic
*
X
• Obtain the p-value
(
p = P dX < d /H0
*
X
)
If the p-value is small, then the null hypothesis is rejected
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
Two-tailed test for the mean
H0 : µ = µ0
H1 : µ ≠ µ0
•P-VALUE APPROACH
• Obtain the test statistic
d
*
X
•Obtain the p-value
(
p = P dX > d /H0
*
X
)
N(0,1)
tn-1
u Normal population, σ is known
u Unknown distribution but σ is
known and n is large
u Normal population, σ is
unknown
If the p-value is small, then the null hypothesis is rejected
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
Two-tailed test for the proportion
H0 : p = p 0
H1 : p ≠ p 0
•P-VALUE APPROACH
• Obtain the test statistic d*
dpˆ =
pˆ − p
p(1− p)
n
≈ N(0,1)
d pˆ
pˆ - p0
p̂
=
≈ N(0,1)
H0
p0 (1- p0 )
n
•n is large
•Obtain the p-value
(
p = P dpˆ > dp*ˆ /H0
)
If the p-value is small, then the null hypothesis is rejected
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
Two-tailed test for the variance
H0 : σ ≥ σ
2
H1 : σ < σ
2
0
2
2
0
•P-VALUE APPROACH
• Obtain the test statistic
dS*
2
•Obtain the p-value
(
p = P dS < d /H0
χ
2
n−
−1
2
*
S2
)
u Normal population
If the p-value is small, then the null hypothesis is rejected
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa
Two-tailed test for the variance
H0 : σ = σ H1 : σ ≠ σ
2
2
0
2
2
0
•P-VALUE APPROACH
• Obtain the test statistic d*
•Obtain the p-value
dS* 2
••
(
d
p = 2 P dS2 < d /H0
*
S2
)
(
*
S2
••
p = 2 P dS2 > dS* 2 /H0
)
If the p-value is small, then the null hypothesis is rejected
Universidad de Oviedo. Facultad de Economía y Empresa. Grado en ADE. Métodos Estadísticos para la
Empresa