Question

I'm confused on how to work this problem.
A sportswriter wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean yardage for Group 1 was x1 = 30 yards with a standard deviation of s₁ = 8 yards. The mean yardage for Group 2 was x2= 26 yards with a standard deviation of s₂ = 6 yards. Assume that the two groups of kicks are independent. Let μ₁ and μ₂ represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled football and an air-filled football. Let σ₁ and σ₂ be the corresponding population standard deviations. Assuming two-sample t procedures are safe to use, what is a 99% confidence interval for μ₁ – μ₂? (Use the conservative value for the degrees of freedom, which is the formula.)

Answer 1

let n, 9, n=9, 21=30, T2-26. SI = 8 32= 6. 99% with (18-2)=16 degree of freedom is 2.921 at at gay. CI = t-shet t o sit in 1 3 2 b + In tha2lnir 30-26 + 2.98 11 (8) 48 + (6) 28 Ja+g-2 1 8 9 4 1 2.92 x 3.33 =) "I 9.74 = (-5-79, 13.74) we are qqq. confident that the difference of population lies in this enterral. two