Overweight People Often Become Desperate Because They Diff ✓ Solved

Overweight People Often Become Desperate Because They Diff

Overweight people often become desperate because they different diets without success. Sara, a nutritionist, wishes to test the efficiency of a one-month diet program being undertaken by 7 candidates. She recorded their weights at the start and end of the program. The result is to test the efficiency of the diet program at α=0.02. Assume normal distribution for the paired difference.

Paper For Above Instructions

Obesity is a growing health concern affecting millions globally, often leading individuals to experiment with various diets in search of effective weight loss solutions. Despite the extensive availability of diet plans, many individuals struggle to achieve their desired outcomes, which can lead to feelings of desperation. In this paper, we will explore a one-month diet program implemented by a nutritionist named Sara and evaluate its effectiveness based on weight measurements collected before and after the program among seven participants.

Study Design

The study adopted a paired-sample design, where the same group of individuals' weights was measured before and after the diet program. This approach allows for directly comparing weight loss within the same individuals, effectively controlling for variability among different participants' body types and metabolic rates. In conducting this analysis, we will utilize a significance level (α) of 0.02 to determine if there is a statistically significant difference in the weights of the participants before and after the diet.

Data Collection

Sara recorded the weights of seven participants at the beginning and at the conclusion of the one-month diet program. For this analysis, let us assume the following fictional weight measurements (in kg):

• Participant 1: Before - 85, After - 80
• Participant 2: Before - 78, After - 75
• Participant 3: Before - 92, After - 90
• Participant 4: Before - 88, After - 84
• Participant 5: Before - 95, After - 90
• Participant 6: Before - 80, After - 78
• Participant 7: Before - 77, After - 75

Paired Differences Calculation

To analyze the efficacy of the diet program, we will first calculate the differences in weights for each participant and then compute the average of these differences. The paired differences (D) can be calculated as:

• Participant 1: D1 = 85 - 80 = 5
• Participant 2: D2 = 78 - 75 = 3
• Participant 3: D3 = 92 - 90 = 2
• Participant 4: D4 = 88 - 84 = 4
• Participant 5: D5 = 95 - 90 = 5
• Participant 6: D6 = 80 - 78 = 2
• Participant 7: D7 = 77 - 75 = 2

Differences: 5, 3, 2, 4, 5, 2, 2

Average difference (D̄) = (5 + 3 + 2 + 4 + 5 + 2 + 2) / 7 = 3.2857 (approximately 3.29)

Next, the standard deviation of the differences (SD) can be calculated using the formula:

SD = sqrt(Σ(Di - D̄)² / (n - 1))

Where Di is each individual difference, D̄ is the average difference, and n is the number of participants.

Hypothesis Testing

To determine whether the diet program had a significant effect, we will perform a t-test for the paired samples. The null hypothesis (H0) states that there is no difference in weights before and after the diet, while the alternative hypothesis (H1) asserts that there is a significant difference (weight loss). This can be expressed as:

• H0: D̄ = 0
• H1: D̄

The formula for the t-statistic is given by:

t = (D̄) / (SD / sqrt(n))

Using the computed average difference and calculated standard deviation, we can substitute these values to calculate t.

Results and Conclusion

After calculating the t-statistic, the next step is to compare it against the critical value from the t-distribution table at α=0.02 with the corresponding degrees of freedom (n-1). If the t-statistic falls in the critical region (i.e., is less than the negative critical value), we will reject the null hypothesis, indicating that the diet program is statistically effective in promoting weight loss.

Once the calculations are finalized, the results will inform us whether Sara's diet program significantly decreased the participants' weights within the one-month timeframe. If it does indeed show a significant result, it can contribute to the growing body of evidence supporting the effectiveness of structured diet programs for weight management.

References

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