The average mpg usage for a 2009 Toyota Prius for a sample o

The average mpg usage for a 2009 Toyota Prius for a sample of 7 tanks of gas was 43.5 with a standard deviation of 1.8. For a 2009 Honda Insight, the average mpg usage for a sample of 7 tanks of gas was 39.9 with a standard deviation of 2.0.

The average mpg usage for a 2009 Toyota Prius for a sample of 7 tanks of gas was 43.5 with a standard deviation of 1.8. For a 2009 Honda Insight, the average mpg usage for a sample of 7 tanks of gas was 39.9 with a standard deviation of 2.0.

H₀: _toy – _hon 0 vs. H₁: _toy – _hon > 0. Reject H₀ if t_calc > 1.782

H₀: _toy – _hon 0 vs. H₁: _toy – _hon > 0. Reject H₀ if t_calc < 1.782

H₀: _toy – _hon 0 vs. H₁: _toy – _hon < 0. Reject H₀ if t_calc < – 1.782

H₀: _toy – _hon 0 vs. H₁: _toy – _hon < 0. Reject H₀ if t_calc > – 1.782

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

Solution

Give f(x) = (0.5) x                0<x<2

Mean = E(x) = x . f(x) dx

                     = x . (0.5) x dx

                      = 0.5 x ² dx

                      = 0.5 [x³ / 3]₀²

                      = 0.5(8/3)

     Mean = 1.3333 µm

in case of continuous distribution median is the point which divides the total area into two equal parts thus if M is the median then

₀^M f(x) dx = 1/2

₀^M     (0.5) x    dx = 1/2

0.5 ₀^M (x) dx = 1/2

(0.5) (x²/2)₀^M = 1/2

(0.5) M² = 1

M² = 1 / 0.5

M² = 2

Median = 1.414

Given n₁ = 7      n₂ = 7     mean(x1) = 43.5 mean (x2) = 39.9   s.d(s1) =1.8 s.d(s2) =2

The null hypothesis is

H₀ : µ_toy - µ_hon 0

Against the alternative hypothesis

H₀ : µ_toy - µ_hon   > 0

The test statistic is

t = (( X₁ - X ₂) /(n₁s1+n₂s2)/n₁+n₂-2) * (1/n₁)+(1/n₂) ) t_(n1+n2-2)

t = (( 43.5 - 39.9) /(7*1.8 + 7*2)/7+7-2) * (1/7)+(1/7) ) t_(7+7-2)

t = 3.6 / 2.2167*0.2858

t= 4.5229

here t_tab   at 0.05 level of significance at 12 degrees of freedom

therefore t_cal    >    t_tab we reject the null hypothesis

therefore the true mean mpg is lower for the honda yes