Question

What hypothesis testing procedure should you use to answer these questions? Assume all samples are simple random samples, and assume α = 0.05 if it isn’t specified. A car company says that the mean gas mileage for its luxury sedan is at least 21 mpg. You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company’s luxury sedans is normally distributed. At α = 0.05, test the company’s claim.

Answer 1

Null hypothesis

vs

Alternative hypothesis

We have for given sample,

Population mean for given sample=21

Sample mean=19

Sample standard deviation s=4

Sample size =n=5

Degree of freedom = n-1 =4

t test statistic formula is

  

=-1.118

P value =0.1631...................by using TDIST(-1.118,4,1) in Excel.

P value 0.1631>0.05

Therefore we fail to reject H0.

Conclusion: We do not have sufficient evidence to say that  the mean gas mileage for its luxury sedan is less than 21 mpg.