Final answer:
To see if the survey supports the hospital's claim, we must construct a 95% confidence interval around the sample's proportion of adults who never take naps. If this interval includes the claim of 75%, the claim is supported; if not, it is not supported.
Step-by-step explanation:
The question pertains to constructing a confidence interval to see if it supports the claim that 75% of all adults never take naps during the day. Given that a random survey finds that 587 out of 675 adults claim never to take naps, we can calculate the sample proportion (p) as 587/675. This will be our point estimate.
To construct a confidence interval, we need to decide the confidence level. Common levels are 90%, 95%, and 99%, but the specific level was not provided in the question, so we'll assume a 95% confidence interval. We would use the formula for the confidence interval for a proportion which is:
p ± z*(√p(1-p)/n), where z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.
Using the standard z-score for a 95% confidence level, which is approximately 1.96, we can calculate the margin of error and hence the confidence interval. If this interval includes 0.75 (the proportion claimed by the hospital), then the survey's findings support the hospital's claim. If not, it does not provide support for the claim.