Answer to Question #99318 in Statistics and Probability for A

Question

**The Walt Disney Company extrapolates data collected from box offices in the United States to determine that 26% of Americans report that their favourite movie is in the Disney collection. They determine that 1,510 respondents in their random sample of 4,872 Americans cite a Disney movie as their favourite. Is the percent of survey respondents who favour a Disney movie significantly greater than the American population?

Answer 1

The 1,510 respondents in a random sample of 4,872 Americans cite a Disney movie as their favorite. That means the percent is

$$\frac {1510}{4872}\times {100 } = {31}$$

According to the terms of the question, the percentage of Walt Disney fans in the United States is 26%. In the sample, this value is 31%, it is 5% more than the US average.

The standard error is

$$\sqrt {\frac{0.31 \times (1-0.31)}{4872}} =0.0066$$

Answer: The percentage of respondents who prefer Disney movie in this sample is significantly greater than that of the US population.