## Problem Description:

The statistical analysis assignment study aims to compare the effectiveness of a new weight loss plan (VLCD) with a traditional one. The null hypothesis suggests no difference in weight loss between the two plans, while the alternative hypothesis proposes a significant difference.

**1. Hypothesis Statements:
**

**Null Hypothesis:**The new weight loss plan is the same as the traditional one (μ_new=μ_traditional).**Alternative Hypothesis:**The new weight loss plan is not the same as the traditional one (μ_new≠μ_traditional).

**2. Data Set: **Please find attached a copy of the spreadsheet.

**3. Descriptive Statistics and Normality Check:
**

Descriptive statistics and histograms were generated for both diet types. The average weight loss for the Traditional VLCD Plan is 10.55 (SD=3.3878), and for the new plan is 12.1 (SD=2.438). The kurtosis and skewness indicate normality for the traditional plan, while the new plan shows a skewed distribution.

**Chart 1: The frequency of the histogram diet vs. weights**

**4. Kolmogorov-Smirnov (KS) Test:
**

**Null Hypothesis:**The data is normally distributed.**Alternative Hypothesis:**The data is not normally distributed.**Result:**Since p-value (0.381) > 0.05, we do not reject the null hypothesis, concluding that the data is normally distributed.

**5. t-Test for Two Independent Samples:
**

- Levene Test suggests unequal variances (p=0.0777).
- A two-sided t-test (p=0.139) indicates no significant difference in weight loss between the traditional and new plans.

**6. Type I and Type II Errors:
**

**Type I Error:**Falsely rejecting the null hypothesis.**Type II Error:**Failing to reject the null hypothesis when it is false.**Prevention:**Minimize α, maximize the power of the test.

## Conclusion

After analysis, no significant difference was found between the two plans. To enhance the study's power and significance, increasing the sample size, using a directional test, and addressing potential confounding variables (exercise, age, sex, smoking) are recommended.