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

`t=(1.20-1.25)/((0.14)/(√(49)))=-2.50`

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=(\bar X-\mu_o)/((s)/(√(n)))` (1)

Calculate the statistic

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

`t=(1.20-1.25)/((0.14)/(√(49)))=-2.50`