Question

A car company claims that its new car, the GoFast2000, has a gas mileage of 35 miles per gallon ( mpg ). A consumer group suspects that the true mean gas mileage of the new cars is less than 35 mpg . The group tests 50 randomly selected Go Fast 2000 cars and finds a sample mean of 34.8 mpg . With all assumptions for inference met, a hypothesis test resulted in a p -value of 0.324.
State the null and alternative hypothesis needed to conduct this test. What test statistic should be used and why? Should any assumption be made about the distribution of MPG? What conclusion can be drawn from the sample results? Test at 0.05 level of significance.

Answer 1

Answer:

H₀: μ = 35 mpg vs. Hₐ: μ < 35 mpg.

A t-test statistic should be used.

The company's claim is correct.

The true mean gas mileage of the new cars is 35 mpg.

Step-by-step explanation:

The consumer group can perform a test for single mean to determine whether the is less than 35 mpg or not.

The hypothesis can be defined as follows:

H₀: The true mean gas mileage of the new cars is 35 mpg, i.e. μ = 35 mpg.

Hₐ: The true mean gas mileage of the new cars is less than 35 mpg, i.e. μ < 35 mpg.

The information provided is:

n = 50

$\bar x$ = 34.8 mpg

As there is no information abut the population standard deviation then we would have to compute the sample standard deviation to estimate the value of σ.

Since the sample standard deviation will be used, a t test statistic would have to be computed.

The test statistic is given by:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$

Assumptions for one sample t-test are:

• Independent samples
• The population is normally distributed
• The sample size should be large enough to make the assumption of normality.

The significance level of the test is, α = 0.05.

The p-value of the test is 0.324.

The decision rule based on p-value is that the null hypothesis will be rejected if the p-value is less than the level of significance and vice-versa.

The p-value = 0.324 > α = 0.05.

As the p-value is more than the significance level the null hypothesis will not be rejected.

Thus, concluding that the company's claim is correct.

The true mean gas mileage of the new cars is 35 mpg.