Question

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

Answer 1

Answer:

$z=\frac{2.14-2.20}{\frac{0.12}{\sqrt{36}}}=-3$  

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

$p_v =P(z$  

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  

$\bar X=2.14$ represent the sample mean

$\sigma=0.12$ represent the population standard deviation

$n=36$ sample size  

$\mu_o =2.20$ represent the value that we want to test  

$\alpha=0.05$ represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

$p_v$ 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:$\mu \geq 2.2$  

Alternative hypothesis:$\mu < 2.2$  

The statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)  

Calculate the statistic  

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

$z=\frac{2.14-2.20}{\frac{0.12}{\sqrt{36}}}=-3$  

P-value  

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

$p_v =P(z$  

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