Question

The average mpg usage for a 2017 Toyota Prius for a sample of 24 tanks of gas was 45.8 with a standard deviation of 1.6. For a 2017 Ford Fusion, the average mpg usage for a sample of 24 tanks of gas was 43.7 with a standard deviation of 2.6.

Assuming equal variances, at α = .01, is the true mean mpg lower for the Ford Fusion?

(a-1) Consider the appropriate hypotheses.

1. H₀: μ_toy – μ_ford ≤ 0 vs. H₁: μ_toy – μ_ford > 0. Reject H₀ if t_calc > 2.410

  
(a-2) Calculate the t_calc. (Round your answer to 4 decimal places.)

t_calc           


(b) Calculate the p-value using Excel. (Round your answer to 4 decimal places.)

p-value           

Answer 1

To test,

Ho:toy-ford0 V\s H1: toy-ford0

Given:

,

s1=1.6 , s2=2.6

n1=24 , n2=24

Use alpha level is 0.01

Test statistic,

Where,

Put given values in above formulae we get,

Sp^2= 4.6599

# Test statistic= 3.3699

# P value= 0.0008

Where P value < 0.01 ( alpha level)

We reject Ho

Conclusion: The true mean mpg lower for the Ford Fusion.