Watch your cholesterol: A sample of 310 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.93 millimole per liter. Assume the population standard deviation is =σ0.17.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Construct a 98% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs. Round the answer to at least two decimal places.A 98% confidence interval for the mean reduction in cholesterol is <<μ.
Question
Watch your cholesterol: A sample of 310 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.93 millimole per liter. Assume the population standard deviation is =σ0.17.Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Construct a 98% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs. Round the answer to at least two decimal places.A 98% confidence interval for the mean reduction in cholesterol is <<μ.
Solution
To construct a 98% confidence interval for the mean reduction in total cholesterol, we first need to know the standard error of the mean. The standard error (SE) is calculated by dividing the standard deviation (σ) by the square root of the sample size (n).
In this case, σ = 0.17 and n = 310.
SE = σ / √n = 0.17 / √310 ≈ 0.0096
Next, we need to find the z-score that corresponds to a 98% confidence interval. The z-score for a 98% confidence interval is approximately 2.33 (you can find this value in a standard z-table or using a calculator).
The margin of error (ME) is then calculated by multiplying the z-score by the standard error.
ME = z * SE = 2.33 * 0.0096 ≈ 0.0224
Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample mean.
Lower limit = mean - ME = 0.93 - 0.0224 ≈ 0.91 Upper limit = mean + ME = 0.93 + 0.0224 ≈ 0.95
So, the 98% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs is approximately (0.91, 0.95).
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