Low-birth-weight babies are at increased risk of respiratory infections in the first few months of life and have low liver stores of vitamin A. In a randomized, double-blind experiment, 55 low-birth-weight babies were randomly divided into two groups. Subjects in group 1 (treatment group, n₁ = 30) were given 25,000 IU of vitamin A on study days 1, 4, and 8; study day 1 was between 36 and 60 hours after delivery. Subjects in group 2 (control group, n₂ = 25) were given a placebo. The treatment group had a mean serum retinol concentration of 45.77 micrograms per deciliter (g/dL), with a standard deviation of 13.42 g/dL.The control group had a mean serum retinol concentration of 15.88 g/dL, with a standard deviation of 7.59 g/dL. It is known that serum retinol concentrations are normally distributed.Determine if there is a difference in the standard deviation of serum retinol concentrations between the treatment group and the control group at the = 0.05 level of significance?

Let₁ denote the standard deviation of serum retinol concentrations for infants receiving vitamin A supplements, and₂ the standard deviation for infants receiving a placebo.

Rejection Region:

We are performing a two-tailed test.

The critical value in the right tail is F_/2 =

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.

The critical value in the left tail is F_1-/2 =

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.

(Report the right-tail value as it appears in the table.Report the left-tail value rounded to 3 decimal places.)

Test Statistic:

The test statistic for this test is F₀ =

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.

Conclusion:

We

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(reject /fail to reject) H₀.

The data

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(does /does not) provide significant evidence of a difference in the standard deviations of serum retinol concentrations between infants who receive vitamin A supplements and those who receive a placebo.

P-Value:

Using Minitab Express, the P-value for this test is

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.