Review Question - QID 217716

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Statistical Measures Confidence Interval (CI) Describes the range in which the mean would be expected to fall if the study were performed again and again QID: 217716 (M1.OMB.4771)

QID 217716 (Type "217716" in App Search)

A team of researchers is evaluating the efficacy of a new drug in lowering low-density lipoprotein (LDL) levels in patients with atherosclerotic cardiovascular disease. They recruited 1,250 patients with atherosclerotic cardiovascular disease for their study. Baseline LDL levels are measured in all patients. Half of the patients were assigned to receive the standard of care (control cohort) while the other half were assigned to receive the standard of care in addition to the new drug (treatment cohort). Six months later, LDL levels are again measured in all patients. In the treatment cohort, the mean change in LDL level was 9.8 mg/dL with a standard deviation (SD) of 2.1 mg/dL. Which of the following best represents the 95% confidence interval for the change in the LDL level of the treatment cohort?

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5.68-13.92

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9.58-10.02

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9.64-9.96

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9.66-9.94

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9.68-9.92

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A 95% confidence interval is defined as the range of values for which there is 95% probability that the true value lies within the range. It is calculated as mean +/- 1.96*SD/sqrt(n of the specified cohort) = 9.8 +/- 1.96*2.1/sqrt(625) = 9.64-9.96.

In general, a confidence interval denotes the range of values for which there is a given probability that the population parameter falls within the range. Put another way, if given a 95% confidence interval for a sample parameter, there is only a 5% chance that the true population parameter falls outside of this range. Confidence intervals are calculated as: mean +/- z*SEM, where z is the z-score and SEM is the standard error of the mean (also known as the standard deviation of the sampling distribution). SEM is calculated as: SEM = SD/sqrt(n). The z-score varies depending on the desired confidence interval and represents the number of standard deviations from the mean. For a 95% confidence interval, z = 1.96, which is often rounded to z = 2 for ease of use. In general, 68% of data values in a normal distribution lie within 1 standard deviation of the mean, 95% of data values lie within 2 standard deviations of the mean, and 99.7% of data values lie within 3 standard deviations of the mean.

Incorrect Answers:
Answer 1: 5.68-13.92 is obtained by the equation: mean +/- 1.96*SD = 9.8 +/- 1.96*2.1. This is incorrect because it inappropriately uses a standard deviation rather than the standard error of the mean (standard deviation of the sampling distribution).

Answer 2: 9.58-10.02 is obtained by the equation: mean +/- 2.58*SD/sqrt(n) = 9.8 +/- 2.58*2.1/sqrt(625). This is incorrect because it denotes the 99% confidence interval (z-score = 2.58).

Answer 4: 9.66-9.94 is obtained by the equation: mean +/- 1.645*SD/sqrt(n) = 9.8 +/- 1.645*2.1/sqrt(625). This is incorrect because it denotes the 90% confidence interval (z-score = 1.645).

Answer 5: 9.68-9.92 is obtained by the equation: mean +/- 1.96*SD/sqrt(n of the total cohort) = 9.8 +/- 1.96*2.1/sqrt(1,250). This is incorrect because it replaces the n of the treatment cohort (625) with the n of the entire cohort (1,250) in the denominator.

Bullet Summary:
The 95% confidence interval is calculated by the following equation: mean +/- 1.96*SD/sqrt(n).

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