Overweight People Often Become Desperate Because They Differ

Overweight People Often Become Desperate Because They Different Diets

Overweight people often become desperate because they undertake different diets without success. Sara, a nutritionist, wishes to test the efficiency of a one-month diet program undertaken by seven candidates. She recorded their weights at the start and end of the program. The results are shown as follows: S.NO, Before, After. The objective is to test the effectiveness of the diet program at a significance level of α=0.02, assuming a normal distribution for the paired differences.

Paper For Above instruction

Introduction

The challenge of weight management is a prevalent concern among overweight individuals, often leading to frustration and despair when dieting efforts fail. To assess the efficacy of a specific diet regimen, a structured statistical analysis can be employed. In this scenario, Sara, a nutritionist, evaluates whether her one-month diet program effectively reduces weight among her seven candidates. The analysis involves statistical hypothesis testing of paired data, comparing weights before and after the intervention, to determine if the observed differences are statistically significant at a 2% significance level.

Methodology

The study utilizes a paired sample t-test, which is appropriate when the same subjects are measured before and after treatment. The core assumptions include the normality of the difference scores, which is assumed in this case, and the independence of pairs. The hypotheses are structured as follows:

- Null hypothesis (H0): There is no difference in mean weights before and after the diet, i.e., μ_d = 0.

- Alternative hypothesis (H1): There is a significant difference, i.e., μ_d ≠ 0.

The significance level is set at α = 0.02, indicating a 2% risk of rejecting the null hypothesis when it is true.

Data and Calculations

Suppose the recorded weights for the seven candidates are as follows:

| S.NO | Before (kg) | After (kg) |

|-------|--------------|------------|

| 1 | x1 | y1 |

| 2 | x2 | y2 |

| 3 | x3 | y3 |

| 4 | x4 | y4 |

| 5 | x5 | y5 |

| 6 | x6 | y6 |

| 7 | x7 | y7 |

The difference for each candidate (d_i) = Before - After:

d_i = x_i - y_i

The mean difference (d̄), standard deviation of differences (s_d), and the t-statistic are calculated as follows:

t = d̄ / (s_d / √n)

where n = 7 (number of pairs).

The critical t-value for a two-tailed test at α=0.02 with degrees of freedom df= n-1=6 is determined from t-distribution tables.

Note: Actual values for these weights are necessary for precise calculations; for this illustration, hypothetical data are considered, or calculations can be performed once the data are provided.

Results and Interpretation

Based on the calculated t-statistic and the critical t-value, the null hypothesis is either rejected or not rejected. If the absolute value of the t-statistic exceeds the critical value, it indicates a statistically significant difference in weights due to the diet program.

Assuming calculations reveal a significant difference, we conclude that the diet is effective in reducing weight at the 2% significance level. Conversely, if no significance is found, the data do not provide sufficient evidence to assert the diet's effectiveness.

Conclusion

The statistical analysis provides crucial insights into the diet program's efficacy. A significant result supports the diet's role in weight reduction; a non-significant result suggests the need for further investigation or alternative strategies. Conducting such analyses enables healthcare professionals to make evidence-based decisions, ultimately aiding in designing better weight management interventions.

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