Question

There seems to be no end to how large the signing bonuses professional athletes can obtain when they start their careers (Peyton Manning - $11.6 million). Suppose a sample of 18 new NFL players report their signing bonuses at the start of the 1998 season, and the results show a mean of $3.81 million and a standard deviation of $1.7 million. Estimate with 90% confidence the mean signing bonus for that season (in millions).

Answer 1

3.113, 4.507

Explanation:

From the given values:

Mean = 3.81

Standard deviation = 1.74

Therefore

M = √(1.72/18) = 0.4

μ = M ± t(sM)

μ = 3.81 ± 1.74*0.4

μ = 3.81 ± 0.697

Recall that the mean is estimated at 90% confidence level,

Hence,

= 90% CI [3.113, 4.507]