Question

4. [9 marks] Tesla announced that its Model 3 electric car can travel, on average, 354 kilometres on a single charge of its battery. Suppose that an automotive research company tests this claim by sampling 6 random Teslas and finds that they travel 350 km, 375 km, 385 km, 390 km, 345 km, and 375 km, respectively, on a single charge.

(a) Determine d, the sample mean driving distance of the Teslas, along with sd, the sample standard deviation in the driving distances (to 3 decimals).

(b) Perform a hypothesis test at an α =0.05 significance level to determine whether the sample provides evidence that the true mean Tesla driving distance is actually greater than the company’s claim of 354 km. Be sure to state the null and alternate hypotheses and show your calculations of the test statistic (to 2 decimals) and the critical region.

Null Hypothesis H0:                                             Alternate Hypothesis Ha:

Observed test statistic:

Critical Region:

Conclusion:

Concluding Statement:

(c) Rounding final results to 3 decimal places, determine an appropriate 100(1 − α)% confidence interval for the true mean driving distance of a Tesla Model 3 if it’s to be used to test the null hypothesis in part (b).

Answer 1