Question

1. Let μ₁ denote true average tread life for a premium brand of P205/65R15 radial tire, and let μ₂ denote the true average tread life for an economy brand of the same size. Test H₀: μ₁ − μ₂ = 5000 versus H_a: μ₁ − μ₂ > 5000 at level 0.01, using the following data: m = 30, x = 42,100, s₁ = 2500, n = 30, y = 36,200, and s₂ = 1500.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

2. State the conclusion in the problem context.

- Fail to reject H₀. The data does not suggest that the difference in average tread life exceeds 5000.

-Reject H₀. The data does not suggest that the difference in average tread life exceeds 5000.    

-Fail to reject H₀. The data suggests that the difference in average tread life exceeds 5000.

-Reject H₀. The data suggests that the difference in average tread life exceeds 5000.

Answer 1

1.) For the premiura hand five * Corx) = 42,100 For the economy hound tire I, (ory) = 36,200 1500 S 2500 Sz na corn) = 30 n, Corm) = 30 Test statistic (Z) = x - x -S4-M2) z - 1.69 = 42160 - 36200-5000 2500 1500² + 30 30 p-value = 0.0455 Source - STATKEY Cimage attached) 2.) As p-value (0.0455) > < (0.01) - Fail to Reject Ho excees 5000, Conclesion- - Fail to Reject Ho. The data does not suggest that the difference in average tread life (1st option).

Statkey Theoretical Distribution Normal Distribution Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 1 0.35 Edit Parameters 0.30 0.25 0.20 0.046 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 3.0 4.0 2.0 1.690 Activate Windows

The test statistic is calculated using the formula mentioned. The p value is obtained from STATKEY (image attached for reference). We compare the p value with alpha and make the required conclusion.