The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Find a 99% confidence interval on the difference in the mean life.Car Brand 1 Brand 21 37734 352022 45299 416353 36240 355004 32100 319505 37210 380156 48360 478007 38200 378108 33500 33215(a) Calculate d=(b) Calculate sD =(c) Calculate a 99% two-sided confidence interval on the difference in mean life.
Accepted Solution
A:
Answer:a) σ = 4933,64b) CI 99% = ( - 5746 ; 7194 )c) No difference in brandsStep-by-step explanation:Brand 1:n₁ = 8x₁ = 38222s₁ = 4974Brand 2:n₂ = 8x₂ = 37498s₂ = 4893As n₁ = n₂ = 8 Small sample we work with t -student tabledegree of freedom df = n₁ + n₂ - 2 df = 8 +8 -2 df = 14CI = 99 % CI = 0,99From t-student table we find t(c) = 2,624CI = ( x₁ - x₂ ) ± t(c) * √σ²/n₁ + σ²/n₂σ² = [( n₁ - 1 ) *s₁² + ( n₂ - 1 ) * s₂² ] / n₁ +n₂ -2σ² = 7* (4974)² + 7*( 4893)² / 14σ² = 24340783 σ = 4933,64√ σ²/n₁ + σ²/n₂ = √ 24340783/8 + 24340783/8√ σ²/n₁ + σ²/n₂ = 2466CI 99% = ( x₁ - x₂ ) ± 2,624* 2466CI 99% = 724 ± 6470CI 99% = ( - 5746 ; 7194 )As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups