Final answer:
The sample size of the Rasmussen Reports survey on college sports and higher education corruption is 1,000 adults. The point estimate for the belief is 52%, with a 3% margin of error. Using this, we can calculate confidence intervals to analyze American adults' beliefs at different levels of confidence.
Step-by-step explanation:
The sample size of the survey conducted by Rasmussen Reports on May 13, 2013, is 1,000 adults. This figure is explicitly mentioned at the beginning of the survey description. The survey's findings, with 95% confidence, are that between 49% to 55% of Americans believe that big-time college sports programs corrupt the process of higher education. This indicates that the margin of error in the survey is 3% (since it is the difference between the point estimate, which is 52%, and one end of the confidence interval, which is 49% or 55%).
Regarding the calculation:
- a. The point estimate is the midpoint of the interval, which is 52%. The error bound is 3%.
- b. Yes, with 95% confidence we cannot conclude that more than half of all American adults believe this, since the interval includes values both less than and greater than 50%.
- c. Using the point estimate and the sample size of 1,000, a 75% confidence interval would be narrower. However, the interval given does not fall below 50%, so with 75% confidence, we can conclude that at least half of American adults believe that major college sports programs corrupt higher education.