Question

to estimate the proportion of all adults who take daily vitamin d supplements, a researcher gathers data and constructs a 90% confidence interval. what exactly does the term \90% confidence\ mean? if the sampling method were to be repeated many times, about 90% of the resulting confidence intervals would contain the true population proportion. the researcher can be 90% confident that the sampling procedure was conducted without bias or error. we can be 90% certain that if many confidence intervals are constructed, a certain percentage will result in the population proportion lying at the midpoint of the interval. about 90% of all possible sample proportions will be within the interval reported for this particular study. the researcher can be 90% confident that the interval contains both the sample proportion and the population proportion.

Explanation:

Confidence level in statistics refers to the long - run frequency. A 90% confidence interval means that if the sampling process is repeated many times, approximately 90% of those intervals will contain the true population parameter (in this case, the population proportion). Sampling procedures can still have bias (so the second option is wrong). The population proportion is not necessarily at the mid - point of the interval (third option wrong). The confidence interval is about the population proportion, not sample proportions (fourth option wrong). Also, the sample proportion is always in the confidence interval (since the confidence interval is calculated around the sample proportion), but the key is about containing the population proportion (fifth option wrong).

Answer:

If the sampling method were to be repeated many times, about 90% of the resulting confidence intervals would contain the true population proportion.