A common claim is that garlic lowers cholesterol levels. In a test of the effectiveness of garlic, 33 subjects were treated with doses of raw garlic, and their cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/mL) have a mean of 0.67 mg/mL and a standard deviation of 20.73 mg/mL.

Construct a 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment.

  1. Procedure:
  2. Assumptions: (select everything that applies)
  3. Unknown parameter:
  4. Point estimate: =mg/mL (Round the answer to 2 decimal places)
  5. Confidence level % and α=\displaystyle \alpha= , also
    •  α2=\displaystyle \frac{\alpha}{{2}}= , and 1α2=\displaystyle {1}-\frac{\alpha}{{2}}=
    • Critical values: (Round the answer to 3 decimal places)
      • left= right=
  6. Margin of error (if applicable): (Round the answer to 2 decimal places)
  7. Lower bound: (Round the answer to 2 decimal places)
  8. Upper bound: (Round the answer to 2 decimal places)
  9. Confidence interval:(, )
  10. Interpretation: We are % confident that the mean net change in LDL cholesterol after the garlic treatment is between mg/mL and mg/mL.
Based on the confidence interval, is it reasonable to believe that the mean net change in LDL cholesterol after the garlic treatment is greater than 10 mg/mL? Explain.
, because 10 mg/mL.