Question

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population is $0.14.
The value of the test statistic for this hypothesis test is:

Answer 1

Answer:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$    

Step-by-step explanation:

Data given and notation  

$\bar X=1.20$ represent the sample mean given

$\sigma = 0.14$ represent the population standard deviation

$n=49$ sample size  

$\mu_o =1.25$ represent the value that we want to test

t would represent the statistic (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean for the gasoline prices is lower than 1.25, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 1.25$  

Alternative hypothesis:$\mu < 1.25$  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

Calculate the statistic

We can replace in formula (1) the info given like this:  

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$