In a randomized, double-blind experiment, 140140 babies were randomly divided in

Question

In a randomized, double-blind experiment,

140140

babies were randomly divided into a treatment group

left parenthesis n 1 equals 70 right parenthesisn1=70

and a control group

left parenthesis n 2 equals 70 right parenthesisn2=70.

After the study, the treatment group had a mean serum retinol concentration of

46.5246.52

micrograms per deciliter

left parenthesis mu g divided by dL right parenthesis(g/dL)

with a standard deviation of

17.67 mu g divided by dL17.67 g/dL,

while the control group had a mean serum retinol concentration of

11.09 mu g divided by dL11.09 g/dL

with a standard deviation of

9.82 mu g divided by dL9.82 g/dL.

Does the treatment group have a higher standard deviation for serum retinol concentration than the control group at the

alpha equals 0.01=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

sigma 11

represent the population standard deviation for the treatment group and

sigma 22

represent the population standard deviation for the control group. State the null and alternative hypotheses for this test.

Upper H 0H0:

mu 11

ModifyingAbove p with caret 1p1

sigma 11

greater than>

equals=

less than<

not equals

sigma 22

mu 22

ModifyingAbove p with caret 2p2

Upper H 1H1:

mu 11

ModifyingAbove p with caret 1p1

sigma 11

equals=

not equals

less than<

greater than>

ModifyingAbove p with caret 2p2

mu 22

sigma 22

Use technology to find the P-value for this test.

The P-value is

nothing.

(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

less than

greater than

the

alpha equals 0.01=0.01

level of significance,

reject

do not reject

the null hypothesis. There

is not

is

sufficient evidence to conclude that the treatment group has a higher standard deviation for serum retinol concentration than the control group at the

alpha equals 0.01=0.01

level of significance.

Explanation / Answer

The null hypothesis is defined as

the treatment group has a equal standard deviation for serum retinol concentration and the control group at the

alpha equals 0.01=0.01

against the alternative hypothesis is

the treatment group has a higher standard deviation for serum retinol concentration than the control group at the

alpha equals 0.01=0.01

By using the EXCEL Add-In software we get

From the p-value we observe that p-value is smaller than 0.01 level of significance therefore we reject the null hypothesis and conclude that

the treatment group has a higher standard deviation for serum retinol concentration than the control group at the

alpha equals 0.01=0.01

F Test for Differences in Two Variances Data Level of Significance 0.01 Larger-Variance Sample Sample Size 70 Sample Variance 17.67 Smaller-Variance Sample Sample Size 70 Sample Variance 9.82 Intermediate Calculations F Test Statistic 1.7994 Population 1 Sample Degrees of Freedom 69 Population 2 Sample Degrees of Freedom 69 Upper-Tail Test Upper Critical Value 1.7609 p-Value 0.0079

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