What proportion of San Luis Obispo (SLO) residents dine at restaurants at least once a week? To investigate, a local high school student, Deidre, decides to conduct a survey. She selects a random sample of adult residents of SLO, asks each participant whether he/she dines at restaurants at least once a week, and records their responses. Then, she uses her data to find a 95% confidence interval for the proportion of SLO adults who dine out at least once a week to be (0.38, 0.44).
a. The 99% confidence interval based on the same data would be:
A. Narrower, because the more confident we are the narrower the interval
B. Wider, because to be more confident we need to widen the interval
C. We need more information to answer this.
b. According to the 95% confidence interval:
A. There is not convincing evidence that less than half of SLO residents dine at restaurants at least once a week, because the interval does not contain 0.50.
B. There is convincing evidence that less than half of SLO residents dine at restaurants at least once a week, because the interval does not contain 0.50.
C. None of the above, because the confidence interval is unrelated to strength of evidence.