Question

In a​ randomized, double-blind​ experiment, 120 babies were randomly divided into a treatment group (n1 =60) and a control group ( n2= 60 right). After the​ study, the treatment group had a mean serum retinol concentration of 47.35 micrograms per deciliter (ug/ dL) with a standard deviation of 17.26 ug/dL​, while the control group had a mean serum retinol concentration of 14.72 ug/dL with a standard deviation of 14.21 ug/ dL. Does the treatment group have a higher standard deviation for serum retinol concentration than the control group at the alpha equals 0.05 level of​ significance? It is known that serum retinol concentration is normally distributed. Use the​ P-value approach to perform the test.

(Let σ1 represent the population standard deviation for the treatment group and σ2 represent the population standard deviation for the control group. State the null and alternative hypotheses for this test.)

Ho:____ ____ ____

H1:____ _____ ____

**options:p(hat)1, u1, o1,

greater than/equal to, =, <,>

p(hat)2, u2, o2

  

  

Answer 1

Sample 1:  
s₁ =    17.26
n₁ =    60
Sample 2:  
s₂ =    14.72
n₂ =    60
α =    0.05

Null and alternative hypothesis:  
Hₒ : σ1 <= σ2
H₁ : σ1 > σ2
Test statistic:  
F = s₁² / s₂² = 1.3749
Degree of freedom:  
df₁ = n₁-1 =    59
df₂ = n₂-1 =    59   
P-value :  
P-value = F.DIST.RT(1.3739, 59,59) = 0.1122

p-value > α, Do not reject the null hypothesis.