Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. Evaluate the data below. Do you think that their cholesterol levels were significantly lowered? (Show all your work i.e. Ho and Ha, p-value, conclusion in words)
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To determine whether the cholesterol levels were significantly lowered by the low-fat diet, we can conduct a statistical analysis. Here are the steps:
1. Hypotheses:
- Null Hypothesis (Ho): The low-fat diet has no effect on reducing cholesterol levels. There is no significant difference between the initial and final cholesterol levels.
- Alternative Hypothesis (Ha): The low-fat diet has a significant effect on reducing cholesterol levels. There is a noticeable difference between the initial and final cholesterol levels.
2. Gather and analyze the data:
We need the initial and final cholesterol levels of the ten individuals who were on the low-fat diet. Let's assume the initial cholesterol levels are represented as X1 and the final levels as X2. Calculate the difference between the initial and final levels for each person (X2 - X1). Then, calculate the average of these differences.
3. Calculate the test statistic:
To determine if the average difference is statistically significant, we need to calculate the t-test statistic. The formula for the t-test statistic is:
t = (mean difference - hypothesized difference) / (standard deviation / sqrt(n))
In our case, the hypothesized difference is 0 (since the null hypothesis assumes no difference), n is 10 (number of observations), and standard deviation can be calculated using the sample data.
4. Determine the degrees of freedom:
The degrees of freedom (df) for a paired t-test is always n - 1. So, in our case, df = 10 - 1 = 9.
5. Calculate the p-value:
Using the t-test statistic and the degrees of freedom, we can determine the p-value using a t-distribution table or a statistical software.
6. Interpret the results:
- If the p-value is less than the chosen significance level (typically 0.05), we reject the null hypothesis. This means that the low-fat diet had a significant effect on reducing cholesterol levels.
- If the p-value is greater than the chosen significance level, we fail to reject the null hypothesis. This means there is not enough evidence to conclude that the low-fat diet significantly lowered cholesterol levels.
Please provide the actual data (initial and final cholesterol levels) for further analysis, and I will guide you through the remaining steps to complete the evaluation.