Question

1. a study reports the mean change in hdl (high - density lipoprotein, or \good\ cholesterol) of adults eating raw garlic six days a week for six months. the margin of error for a 95% confidence interval is given as plus or minus 6 milligrams per deciliter of blood (mg/dl). this means that a) there is a 95% probability that the true population mean is within 6 mg/dl. b) 95% percent of the population has changed their hdl after eating raw garlic six days a week for six months. c) the study used a method that gives a results within 6 mg/dl of the truth about the population in 95% of all samples. d) we could be certain that the study result is within 6 mg/dl of the truth about the population if the conditions for inferences were satisfied. e) we can be certain that the study results is within 6 mg/dl of the truth about the population.

Explanation:

A confidence interval is a range of values within which we are reasonably certain the true population parameter lies. A 95% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, approximately 95% of those intervals would contain the true population parameter.

Option A is incorrect because it misinterprets the confidence level as a probability for a single interval. Option B is incorrect as it wrongly attributes the 95% to the population changing. Option C is incorrect as it's about samples, not the population. Option E is incorrect as "certain" is too strong; confidence intervals don't guarantee certainty. Option D is correct as confidence interval validity depends on inference conditions (like random sampling, normality if sample size is small etc.) being met.

Answer:

D. We could be certain that the study result is within 6 mg/dl of the truth about the population if the conditions for inferences were satisfied.