Question

Toyota advertises that their Toyota Highlander Hybrid provide 28 MPG. To test this, an experiment involving a sample of 20 Toyota Highlander Hybrid vehicles is conducted. In this experiment, for every vehicle, the MPG in the vehicle's computer while it was set at 60 miles per hour on cruise control is recorded. The sample mean MPG recorded is 28.8 miles per gallon with a standard deviation of 6.89 miles per gallon. Use this information to conduct the following hypothesis test at 0.01 level of significance:
Null hypothesis: The population mean MPG of Toyota Highlander Hybrid vehicles is equal to 28 miles per gallon.

Alternative hypothesis: The population mean MPG is Toyota Highlander Hybrid vehicles is not equal to 28 miles per gallon.

What is your conclusion from this test?

a. do not reject the null

b. accept the null

c. reject the null

d. none of these

Answer 1

Answer:

We accept the null hypothesis.    

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 28.8 miles per gallon

Sample size, n = 120

Alpha, α = 0.01

Sample standard deviation, σ = 6.89 miles per gallon

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 28\text{ miles per gallon.}\\H_A: \mu \neq 28\text{ miles per gallon.}$

We use Two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.8 - 28}{\frac{6.89}{\sqrt{19}} } = 0.5061$

Now, $t_{critical} \text{ at 0.01 level of significance, 19 degree of freedom } =\pm 2.8609$ Since,            

$-2.609 < t_{stat} < 2.8609$

We fail to reject the null hypothesis and accept it.

We accept the null hypothesis and the population mean MPG of Toyota Highlander Hybrid vehicles is equal to 28 miles per gallon.