QuestionCalculate the weighted mean depression levels: Group 1 $\mu_{1}=15$ , Group 2 $\mu_{2}=11$ . Then for alcohol: Group 1 $\mu_{1}=16$ , Group 2 $\mu_{2}=18$ . Round to one decimal place. $\mu=$

Studdy Solution

STEP 1

Assumptions1. The first group has12 women with a mean depression level of15 (CES-D test) and a mean score of16 (MA test). . The second group has8 women with a mean depression level of11 (CES-D test) and a mean score of18 (MA test).
3. The weighted mean is calculated by multiplying each group's mean by its size, summing these products, and then dividing by the total size of both groups.

STEP 2

First, we will calculate the weighted mean for the depression levels from the CES-D test. The formula for the weighted mean is $\mu = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}$ where $w_i$ is the weight (or size) of each group and $x_i$ is the mean of each group.

STEP 3

Now, plug in the given values for the sizes and means of the two groups to calculate the weighted mean for the CES-D test.
$\mu = \frac{(12 \times15) + (8 \times11)}{12 +8}$

STEP 4

Perform the multiplication in the numerator.
$\mu = \frac{180 +88}{20}$

STEP 5

Perform the addition in the numerator and the denominator.
$\mu = \frac{268}{20}$

STEP 6

Perform the division to calculate the weighted mean for the CES-D test.
$\mu =13.4$

STEP 7

Next, we will calculate the weighted mean for the scores from the MAST test. Again, plug in the given values for the sizes and means of the two groups.
$\mu = \frac{(12 \times16) + ( \times18)}{12 +}$

STEP 8

Perform the multiplication in the numerator.
$\mu = \frac{192 +144}{20}$

STEP 9

Perform the addition in the numerator and the denominator.
$\mu = \frac{336}{20}$

STEP 10

Perform the division to calculate the weighted mean for the MAST test.
$\mu =16.8$ The weighted mean depression level from the CES-D test for the combined group is13.4, which is closer to15 than to. The weighted mean score from the MAST test for the combined group is16.8.

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QuestionCalculate the weighted mean depression levels: Group 1 $\mu_{1}=15$ , Group 2 $\mu_{2}=11$ . Then for alcohol: Group 1 $\mu_{1}=16$ , Group 2 $\mu_{2}=18$ . Round to one decimal place. $\mu=$

Studdy Solution

STEP 1

STEP 2

First, we will calculate the weighted mean for the depression levels from the CES-D test. The formula for the weighted mean is $\mu = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}$ where $w_i$ is the weight (or size) of each group and $x_i$ is the mean of each group.

STEP 3

Now, plug in the given values for the sizes and means of the two groups to calculate the weighted mean for the CES-D test.
$\mu = \frac{(12 \times15) + (8 \times11)}{12 +8}$

STEP 4

Perform the multiplication in the numerator.
$\mu = \frac{180 +88}{20}$

STEP 5

Perform the addition in the numerator and the denominator.
$\mu = \frac{268}{20}$

STEP 6

Perform the division to calculate the weighted mean for the CES-D test.
$\mu =13.4$

STEP 7

Next, we will calculate the weighted mean for the scores from the MAST test. Again, plug in the given values for the sizes and means of the two groups.
$\mu = \frac{(12 \times16) + ( \times18)}{12 +}$

STEP 8

Perform the multiplication in the numerator.
$\mu = \frac{192 +144}{20}$

STEP 9

Perform the addition in the numerator and the denominator.
$\mu = \frac{336}{20}$

STEP 10

Perform the division to calculate the weighted mean for the MAST test.
$\mu =16.8$ The weighted mean depression level from the CES-D test for the combined group is13.4, which is closer to15 than to. The weighted mean score from the MAST test for the combined group is16.8.

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QuestionCalculate the weighted mean depression levels: Group 1 μ1=15\mu_{1}=15μ1​=15, Group 2 μ2=11\mu_{2}=11μ2​=11. Then for alcohol: Group 1 μ1=16\mu_{1}=16μ1​=16, Group 2 μ2=18\mu_{2}=18μ2​=18. Round to one decimal place. μ=\mu= μ=

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the sizes and means of the two groups to calculate the weighted mean for the CES-D test.μ=(12×15)+(8×11)12+8\mu = \frac{(12 \times15) + (8 \times11)}{12 +8}μ=12+8(12×15)+(8×11)​

STEP 4

Perform the multiplication in the numerator.μ=180+8820\mu = \frac{180 +88}{20}μ=20180+88​

STEP 5

Perform the addition in the numerator and the denominator.μ=26820\mu = \frac{268}{20}μ=20268​

STEP 6

Perform the division to calculate the weighted mean for the CES-D test.μ=13.4\mu =13.4μ=13.4

STEP 7

Next, we will calculate the weighted mean for the scores from the MAST test. Again, plug in the given values for the sizes and means of the two groups.μ=(12×16)+(×18)12+\mu = \frac{(12 \times16) + ( \times18)}{12 +}μ=12+(12×16)+(×18)​

STEP 8

Perform the multiplication in the numerator.μ=192+14420\mu = \frac{192 +144}{20}μ=20192+144​

STEP 9

Perform the addition in the numerator and the denominator.μ=33620\mu = \frac{336}{20}μ=20336​

STEP 10

Perform the division to calculate the weighted mean for the MAST test.μ=16.8\mu =16.8μ=16.8The weighted mean depression level from the CES-D test for the combined group is13.4, which is closer to15 than to. The weighted mean score from the MAST test for the combined group is16.8.

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QuestionCalculate the weighted mean depression levels: Group 1 $\mu_{1}=15$ , Group 2 $\mu_{2}=11$ . Then for alcohol: Group 1 $\mu_{1}=16$ , Group 2 $\mu_{2}=18$ . Round to one decimal place. $\mu=$

Now, plug in the given values for the sizes and means of the two groups to calculate the weighted mean for the CES-D test.
$\mu = \frac{(12 \times15) + (8 \times11)}{12 +8}$

Perform the multiplication in the numerator.
$\mu = \frac{180 +88}{20}$

Perform the addition in the numerator and the denominator.
$\mu = \frac{268}{20}$

Perform the division to calculate the weighted mean for the CES-D test.
$\mu =13.4$

Next, we will calculate the weighted mean for the scores from the MAST test. Again, plug in the given values for the sizes and means of the two groups.
$\mu = \frac{(12 \times16) + ( \times18)}{12 +}$

Perform the multiplication in the numerator.
$\mu = \frac{192 +144}{20}$

Perform the addition in the numerator and the denominator.
$\mu = \frac{336}{20}$

Perform the division to calculate the weighted mean for the MAST test.
$\mu =16.8$ The weighted mean depression level from the CES-D test for the combined group is13.4, which is closer to15 than to. The weighted mean score from the MAST test for the combined group is16.8.