Question

There is a new type of SUV named Spiderman coming to the market. The manufacturer claims that the average mpg of Spiderman cars is 32 mpg. A consumer group randomly selects 9 Spiderman cars from car dealerships, testing gas mileage under similar conditions. The results are below:

MPG: 31, 27, 33, 27, 35, 28, 29, 31, 29

Could the true average mpg of all Spiderman cars be 32, or are these results too low to be explained by chance? Use the 5 step hypothesis test format.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 32
Alternative Hypothesis, Ha: μ < 32

Rejection Region
This is left tailed test, for α = 0.05 and df = 8
Critical value of t is -1.86.
Hence reject H0 if t < -1.86

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (30 - 32)/(2.7386/sqrt(9))
t = -2.191

P-value Approach
P-value = 0.0299
As P-value < 0.05, reject the null hypothesis.

Here, significance level is not given, so consider 0.05