In a randomized, double-blind experiment,
80
babies were randomly divided into a treatment group
n1=40
and a control group
n2=40.
After the study, the treatment group had a mean serum retinol concentration of
41.85
micrograms per deciliter
(μg/dL)
with a standard deviation of
17.63 μg/dL,
while the control group had a mean serum retinol concentration of
12.04 μg/dL
with a standard deviation of
13.47 μg/dL.
Does the treatment group have a higher standard deviation for serum retinol concentration than the control group at the
α=0.01
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.
H0:
sigma 1σ1
mu 1μ1
sigma 1σ1
ModifyingAbove p with caret 1p1
equals=
greater than>
equals=
less than<
not equals≠
sigma 2σ2
mu 2μ2
ModifyingAbove p with caret 2p2
sigma 2σ2
H1:
sigma 1σ1
mu 1μ1
ModifyingAbove p with caret 1p1
sigma 1σ1
greater than>
greater than>
not equals≠
equals=
less than<
sigma 2σ2
ModifyingAbove p with caret 2p2
sigma 2σ2
mu 2μ2
Use technology to find the P-value for this test.
(Round to three decimal places as needed.)
Make a statement regarding the null hypothesis and draw a conclusion for this test.
Since the P-value is
the
α=0.01
level of significance,
the null hypothesis. There
sufficient evidence to conclude that the treatment group has a higher standard deviation for serum retinol concentration than the control group at the
α=0.01
level of significance.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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