Question

In a random sample of 173 NFL games, Matthew has correctly predicted the winner in 100 of those games. Please show all work/calculations. a) Create a 92% confidence interval for the proportion of NFL games Matthew correctly predicts. Round the end points to the nearest 0.001. b) Based on your confidence interval, is it likely that Matthew picks NFL winners more than half the time? Explain why or why not, using your knowledge of confidence intervals.

Answer 1

a)

Sample proportion = 100 / 173 = 0.578

92% confidence interval for p is

- Z * sqrt ( ( 1 - ) / n) < p < + Z * sqrt ( ( 1 - ) / n)

0.578 - 1.7507 * sqrt( 0.578 * 0.422 / 173) < p < 0.578 + 1.7507 * sqrt( 0.578 * 0.422 / 173)

0.512 < p < 0.644

92% CI for p is ( 0.512 , 0.644 )

b)

Since claimed proportion 0.50 is not included in confidence interval, We have sufficient evidence to support

the claim that it is likely that Matthew picks NFL winners more than half the time.