Question

A national survey of 1,000 adults was conducted by Rasmussen Reports. It concluded with 95% confidence that 49% to 55% of Americans believe that big-time college sports programs corrupt the process of higher education. Part (a) Find the point estimate and the error bound for this confidence interval. (Enter your answers to two decimal places.) point estimate error bound Part (b) Can we (with 95% confidence) conclude that more than half of all American adults believe this? Yes, because the point estimate is above 50%. No, because the confidence interval includes values below 50%, so the population parameter could be less than 50%. Part (c) Use the point estimate from part (a) and n = 1,000 to calculate a 75% confidence interval for the proportion of American adults that believe that major college sports programs corrupt higher education. (Round your answers to three decimal places.) , Part (d) Can we (with 75% confidence) conclude that at least half of all American adults believe this? Yes, because 50% is below the confidence interval, so the population parameter could be above 50%. No, the confidence level is too low to make a prediction about the population parameter.

Answer 1

(a) Here point estimate = (55% + 49%)/2 = 52% = 0.52

Error bound = 55% - 52% = 3% = 0.03

(b) As the confidence interval includes the value of 50%, So the answer is No, because the confidence interval includes values below 50%, so the population parameter could be less than 50%.

(c) 75% confidence interval for the proportion of American adults = p^ +- Z_75% sqrt[0.52 * (1 - 0.52)/1000]

= 0.52 +- 0.0158 * 1.15

= (0.502, 0.538)

(d) Here Yes, because 50% is below the confidence interval, so the population parameter could be above 50%.