Questions: Question 18 (4 points) Abel is a physician who specializes in weight control and wants to compare three types of weight loss programs. He randomly assigned 15 people to his three diet programs (5 people for each program). He measured how much weight they lost in 4 months and compared the three means. Which of these best describes Abel's study? a) quasi-experimental, between subject design b) quasi-experimental, within subject design c) true experimental, between subject design d) true experimental, within subject design

Question 18 (4 points) Abel is a physician who specializes in weight control and wants to compare three types of weight loss programs. He randomly assigned 15 people to his three diet programs (5 people for each program). He measured how much weight they lost in 4 months and compared the three means. Which of these best describes Abel's study? a) quasi-experimental, between subject design b) quasi-experimental, within subject design c) true experimental, between subject design d) true experimental, within subject design
Transcript text: Question 18 (4 points) Listen Abel is a physician who specializes in weight control and wants to compare three types of weight loss programs. He randomly assigned 15 people to his three diet programs (5 people for each program). He measured how much weight they lost in 4 months and compared the three means. Which of these best describes Abel's study? a) quasi-experimental, between subject design b) quasi-experimental, within subject design c) true experimental, between subject design d) true experimental, within subject design
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Solution

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Solution Steps

Step 1: Calculate Sum of Squares Between Groups

The sum of squares between groups (\(SS_{between}\)) is calculated as follows:

\[ SS_{between} = \sum_{i=1}^k n_i (\bar{X}_i - \bar{X})^2 = 2.2013 \]

Step 2: Calculate Sum of Squares Within Groups

The sum of squares within groups (\(SS_{within}\)) is calculated as:

\[ SS_{within} = \sum_{i=1}^k \sum_{j=1}^{n_i} (X_{ij} - \bar{X}_i)^2 = 1.228 \]

Step 3: Calculate Mean Squares

The mean square between groups (\(MS_{between}\)) and mean square within groups (\(MS_{within}\)) are calculated as follows:

\[ MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{2.2013}{2} = 1.1007 \]

\[ MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{1.228}{12} = 0.1023 \]

Step 4: Calculate F-statistic

The F-statistic is calculated using the mean squares:

\[ F = \frac{MS_{between}}{MS_{within}} = \frac{1.1007}{0.1023} = 10.7557 \]

Step 5: Calculate P-value

The p-value is calculated using the F-distribution:

\[ P = 1 - F(F_{observed}; df_{between}, df_{within}) = 1 - F(10.7557; 2, 12) = 0.0021 \]

Step 6: Report Degrees of Freedom

The degrees of freedom for the analysis are:

\[ df_{between} = 2 \] \[ df_{within} = 12 \]

Final Answer

Based on the analysis, the results are summarized as follows:

  • Degrees of Freedom Between Groups: \(2\)
  • Degrees of Freedom Within Groups: \(12\)
  • F-statistic: \(10.7557\)
  • P-value: \(0.0021\)
  • Mean Square Between Groups: \(1.1007\)
  • Mean Square Within Groups: \(0.1023\)

The best description of Abel's study is:

\(\boxed{c}\)

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