The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population (s) is $0.12. At 95% confidence, test the company's claim. The hypotheses are:H0: m 2.20Ha: m < 2.20If the test is done at 95% confidence, the null hypothesis should

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 2.2$ per gallon

Step-by-step explanation:

Data given and notation

[tex]\bar X=2.14[/tex] represent the sample mean

[tex]\sigma=0.12[/tex] represent the population standard deviation

[tex]n=36[/tex] sample size

[tex]\mu_o =2.20[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value for the test (variable of interest)

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for the prices is less than 2.20, the system of hypothesis are:

Null hypothesis:[tex]\mu \geq 2.2[/tex]

Alternative hypothesis:[tex]\mu < 2.2[/tex]

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)

Calculate the statistic

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

[tex]z=\frac{2.14-2.20}{\frac{0.12}{\sqrt{36}}}=-3[/tex]

P-value

Since is a one sided lower test the p value would be:

[tex]p_v =P(z<-3)=0.00135[/tex]

Conclusion

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 2.2$ per gallon