The leader of two postpartum women's support groups is interested in the depression levels of the women in her groups. She administers the Center for Epidemiologic Studies Depression Scale (CES-D) screening test to the members of her groups. The CES-D is a 20-question self-test that measures depressive feelings and behaviors durin the previous week. The mean depression level from the screening test for the 6 women in the first group is mu_1 = 16; the mean depression level for the 10 women in the second group is mu_2 = 12. Without calculating the weighted mean for the combined group, you know that the weighted mean is: Midway between 16 and 12 Closer to 16 than to 12 Closer to 12 than to 16 Compute the weighted mean. Enter your answer rounded to one decimal place. mu = The support group leader realizes that she should also screen for alcohol abuse, so she gives the women in her two groups the Michigan Alcohol Screening Test (MAST). The MAST is a 22-question self-test focusing on the use and abuse of alcohol. The first group has a mean score of mu_1 = 18. The second group has a mean score of mu_2 = 14. Compute the weighted mean. Enter your answer rounded to one decimal place. mu =

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The mean depression level  for the first group is μ₁ = 16.

The mean depression level for the second group is μ₂ = 12

The weighted mean is closer to 12 than to 16.

The calculated weighted mean  for  CES-D is 13.5

The calculated weighted mean  for  MAST is 17.25 ≈ 17.0 rounded to 17.

Calculating the weighted mean μ

μ=   [tex]\frac{w1x1 + w2x2}{w1+w2}[/tex]      {where x1 =μ₁ and x2= μ₂ }

μ= 16×6 + 10×12/ 6+10

μ= 216/16

μ= 13.5

The first group has a mean score of μ₁= 18.

The second group has a mean score of μ₂ = 14

Calculating the weighted mean μ

{where x1 =μ₁ and x2= μ₂ ; w1= number of women in the first   group and w2= number of women in the second group}

μ=   [tex]\frac{w1x1 + w2x2}{w1+w2}[/tex]      

μ= 18×6 + 14×12/ 6+10

μ= 276/16

μ= 17.25≈ 17

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