In a test of of garlic for lowering cholesterol, 45 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured beforeandafter the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have a mean of 5.4 and a sd of 17.5. Construct a 90% confidence interval est. of the mean net change in LDL cholesterol. after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
What is the confidence interval of the mean u?
___Mg/dL < u < ___Mg/dL
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
(±.05) and its Z score.
90% = mean ± Z (SEm)
SEm = SD/√n
To construct a confidence interval for the mean net change in LDL cholesterol after the garlic treatment, we can use the following formula:
Confidence Interval = Mean ± (Z * (Standard Deviation / √n))
In this case, we are given:
Mean (x̄) = 5.4 mg/dL (mean net change)
Standard Deviation (s) = 17.5 mg/dL
Sample size (n) = 45 (number of subjects)
Confidence level (C) = 90%
First, we need to calculate the critical value (Z) corresponding to the confidence level. Since the sample size (n) is larger than 30, we can use the Z-distribution. The Z-value for a 90% confidence level is approximately 1.645.
Substituting the values into the formula, we get:
Confidence Interval = 5.4 ± (1.645 * (17.5 / √45))
Now, let's compute the interval:
Confidence Interval = 5.4 ± (1.645 * (17.5 / √45))
Confidence Interval ≈ 5.4 ± (1.645 * 2.607)
Confidence Interval ≈ 5.4 ± 4.287
Confidence Interval ≈ (1.113, 9.687) mg/dL
Therefore, the confidence interval of the mean net change in LDL cholesterol after the garlic treatment is approximately (1.113, 9.687) mg/dL.
Now, to interpret the confidence interval, we can say that we are 90% confident that the true mean net change in LDL cholesterol, u, falls within the range of 1.113 mg/dL to 9.687 mg/dL. This means that if we were to repeat the study numerous times and construct 90% confidence intervals from each sample, approximately 90% of those intervals would contain the true population mean net change in LDL cholesterol after the garlic treatment.
As for the effectiveness of garlic in reducing LDL cholesterol, since the confidence interval does not include zero (which represents no change), it suggests that the garlic treatment has a statistically significant effect on reducing LDL cholesterol. However, further studies and analysis would be required to fully evaluate its clinical significance and effectiveness.