Question

Greg wants to compare the top speed of the fastest cars in the world to determine which car is faster, the Hennessy Venom GT or the Bugatti Veyron. He gets the guys from Top Gear to take the cars on the track to determine if one car is faster than the other. Since the cars are privately owned, they only allow for 5 test runs. Is the venom significantly faster than the Bugatti?

Trial   1   2   3   4   5              

Bugatti 267  268  268   268  268

Venom 268  268  269   270  270

a. State the question you would like to answer, your null and alternative hypotheses

b. Calculations: Include t score and p-value

c. Conclusion: Rejection decision, why, and answer to the question.

Answer 1

on Given data we alculate values: (1) The provided sample means are : X̅1 = 267.8 X̅2 = 269.0 and the known population standard deviations are : S1 = 0.447 S2 = 1.0 and the sample size are n1 = 5 and n2 = 5. (2) Our test hypothesis is : The following null and alternative hypothesis need to be tested, μ1 = Bhugati speed mean   μ2= Venom speed mean hypothesis = h0: μ1 = μ2 vs H1: μ1 < μ2 This hypothesis corresponds to a lower tailed, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (3) Test statistics : The calculation of the t-test proceeds as follows, z = X̅1 - X̅2 267.8 - 269.0 ---------------------- = -------------------------------- = -2.4497 √(σ1²/n1)+(σ2²/n2) √(0.447²/5) + (1.0²/5) (4) Rejection Criteria : Based on the information provided, the significance level is α = 0.05,and the degrees of freedom are df= 8 and the critical value for a lower tailed test is t tabulated = 1.8595 And the rejection region for this upper-tailed test is R =[t: t < -1.8595] (5) Decision about the null hypothesis : Since it is observed that t calculated means t = -2.4497 < tabulated = -1.8595 it is then concluded that the null hypothesis is Rejected. Using the P-value approach: The p-value 0.02, and since p = 0.02 < α = 0.05 it is then concluded that the null hypothesis is Rejected. (6) Conclusion It is concluded that the null hypothesis Ho is Rejected. Therefore, there is enough evidence to claim that population mean μ2 is greater than μ1 , at the 0.05 significance level.