Upper tail or lower tail test?

Question

Test the hypothesis that the miles per gallon decreases as the horsepower increases when all other variables are held constant. Use α = 0.10. If miles per gallon is the dependent variable and horsepower is one of the independent variables, would I use a lower tail or upper tail t test?

Answer 1

Edward,

 

In these types of studies, the null hypothesis typically states that the sample mean (the average of the sample data collected) is equal to the mean of the population.

 

We can write this as:

 

H₀: μ = μ_p

 

The alternative hypothesis, H₁ (that fuel economy decreases with increasing horsepower) is that our sample mean will be less than the population value or:

 

H₁: μ < μ_p

 

In a one-tailed test, we're only interested in one-half of the distribution.  The alternative hypothesis tells us which one.

 

Since we want to know if our sample mean is significantly less than the population mean, then we'd only be interested in the left portion (lower) of the distribution.  All .10 of of α lies at the left side.  If the test statistic we calculate falls within that lower .10, then our alternative hypothesis is supported.

 

Hope this helps!