Question

to learn more about the proportion of college students who drink coffee at least once per day, a researcher surveys a random sample of 500 students and constructs a 95% confidence interval based on survey responses. what information does this confidence interval provide? the interval summarizes the proportion of coffee drinkers that would be expected if many new random samples of 500 students were taken. the interval identifies the middle 95% of the distribution of sample proportions that would occur if the sampling method were repeated many times. the interval describes a range of plausible values for the actual proportion of all college students who drink coffee at least once per day. the interval gives the probability that the proportion of daily coffee drinkers among the sample of size 500 will be between the upper and lower bounds of the interval. the interval estimates how individual coffee - drinking habits vary among students in the sample.

Explanation:

A confidence interval is used to estimate an unknown population parameter. In this case, the population parameter is the proportion of all college students who drink coffee at least once per day. 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 proportion. It is not about the sample proportion (except in the context of estimating the population proportion), nor is it about summarizing multiple new samples in the way the first option suggests. The second option is about the sampling distribution of the sample proportion (which is used to construct the confidence interval but is not the interpretation of the confidence interval itself). The fourth option is incorrect because the confidence interval is about the population proportion, not the sample proportion's probability within the interval. The fifth option is wrong as it's not about individual - level variation in the sample.

Answer:

The interval describes a range of plausible values for the actual proportion of all college students who drink coffee at least once per day.